// Numbas version: exam_results_page_options
{"name": "Numbastest uke 40: Funksjonsdr\u00f8fting", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Generelle derivasjonsregler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p><strong>Deriver funksjonene under.</strong></p>\n<p>Merk: For &aring; skrive inn f.eks. $\\frac{1}{x^3}$ b&oslash;r man skrive 1/(x^3), for &aring; skrive inn $\\cos^2x$ b&oslash;r man skrive (cos(x))^2. Bruk * n&aring;r det skal v&aelig;re et produkt mellom to bokstaver.</p>", "advice": "<p>Bruk f&oslash;lgende generelle derivasjonsregler</p>\n<p>$f(x)=a\\cdot u(x)$ gir $f'(x)=a\\cdot u'(x)$ ($a$ er et konstant)</p>\n<p>$f(x)=u(x)+v(x)$ gir $f'(x)=u'(x)+v'(x)$&nbsp;</p>\n<p>$f(x)=u(x)-v(x)$ gir $f'(x)=u'(x)-v'(x)$&nbsp;</p>\n<p>$f(x)=u(x)\\cdot v(x)$ gir $f'(x)=u'(x)\\cdot v(x)+u(x)\\cdot v'(x)$&nbsp; (produktregelen)</p>\n<p>$f(x)=\\dfrac{u(x)}{v(x)}$ gir $f'(x)=\\dfrac{u'(x)\\cdot v(x)-u(x)\\cdot v'(x)}{v^2(x)}$ (br&oslash;kregelen)</p>\n<p>$f(x)=g(u(x))$ gir $f'(x)=g'(u(x))\\cdot u'(x)$ (kjerneregelen)</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"inp1": {"name": "inp1", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out1": {"name": "out1", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..33)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k3": {"name": "k3", "group": "Ungrouped variables", "definition": "random(5..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k4": {"name": "k4", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k5": {"name": "k5", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k6": {"name": "k6", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k7": {"name": "k7", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k8": {"name": "k8", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "inp2": {"name": "inp2", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp3": {"name": "inp3", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp4": {"name": "inp4", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp5": {"name": "inp5", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp6": {"name": "inp6", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp7": {"name": "inp7", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp8": {"name": "inp8", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out2": {"name": "out2", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out3": {"name": "out3", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out4": {"name": "out4", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out5": {"name": "out5", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out6": {"name": "out6", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out7": {"name": "out7", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out8": {"name": "out8", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["inp1", "out1", "k1", "a", "k2", "k3", "k4", "k5", "k6", "k7", "k8", "inp2", "inp3", "inp4", "inp5", "inp6", "inp7", "inp8", "out2", "out3", "out4", "out5", "out6", "out7", "out8"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out1}}(\\simplify{{inp1}})=\\simplify{{k1}*sin({inp1})-{k2-1}*{inp1}^{{a}}+1/{inp1}}$</p>\n<p>$\\simplify{{out1}}'(\\simplify{{inp1}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k1}*cos({inp1})-{a*(k2-1)}*{inp1}^({a-1})-1/({inp1}^2)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out2}}(\\simplify{{inp2}})=\\var{inp2}^{\\var{k2}}\\cdot\\ln \\var{inp2}+\\var{k3+5}$</p>\n<p>$\\simplify{{out2}}'(\\simplify{{inp2}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k2}*{inp2}^({k2-1})*ln({inp2})+{inp2}^({k2-1})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out3}}(\\simplify{{inp3}})=\\var{k3}^\\var{inp3}\\cos(\\var{inp3})$</p>\n<p>$\\simplify{{out3}}'(\\simplify{{inp3}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k3}^{inp3}*ln({k3})*cos({inp3})-{k3}^{inp3}*sin({inp3})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out4}}(\\simplify{{inp4}})=\\dfrac{\\cos(\\var{inp4})}{\\sin(\\var{inp4})}$</p>\n<p>$\\simplify{{out4}}'(\\simplify{{inp4}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(-(cos({inp4}))^2-(sin({inp4}))^2)/((sin({inp4}))^2)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out5}}(\\simplify{{inp5}})=\\dfrac{\\var{inp5}^{\\var{k5}}}{\\var{inp5}^{\\var{k2-3}}+\\var{inp5}^{\\var{k1-1}}}$</p>\n<p>$\\simplify{{out5}}'(\\simplify{{inp5}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({k5}*{inp5}^({k5}-1)*({inp5}^({k2}-3) +{inp5}^({k1}-1))- {inp5}^({k5})*(({k2}-3)*{inp5}^({k2}-4)+({k1}-1)*{inp5}^({k1}-2)))/(( {inp5}^({k2}-3) +{inp5}^({k1}-1))^2)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out6}}(\\simplify{{inp6}})=(\\simplify{{inp6}^{{k6}}+{inp6}+{k7}})(\\simplify{{inp6}^{{k7-2}}+{inp6}})$</p>\n<p>$\\simplify{{out6}}'(\\simplify{{inp6}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({k6}*{inp6}^({k6}-1)+1)*({inp6}^({k7}-2)+{inp6})+({inp6}^({k6})+{inp6}+{k7})*(({k7}-2)*{inp6}^({k7}-3)+1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out7}}(\\simplify{{inp7}})=(\\var{k2}+\\var{inp7}^{\\var{k4}})^{\\var{k6}}$</p>\n<p>$\\simplify{{out7}}'(\\simplify{{inp7}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k4}*{k6}*({inp7}^({k4}-1))*(({k2}+{inp7}^({k4}))^({k6-1}))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out8}}(\\simplify{{inp8}})=\\cos(\\simplify{{inp8}^{{k8}}+{inp8}+{k1}})$</p>\n<p>$\\simplify{{out8}}'(\\simplify{{inp8}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-sin({inp8}^({k8})+{inp8}+{k1})*({k8}*{inp8}^({k8}-1)+1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Funksjonsdr\u00f8fting", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Det er gitt en funksjon $f(x)=\\simplify{{a}*x^3-{a*k^2}x}$ som er definert for alle $x\\in\\mathbb{R}$</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "xmin": {"name": "xmin", "group": "Ungrouped variables", "definition": "if(a>0,expression('x2'),expression('x1'))", "description": "", "templateType": "anything", "can_override": false}, "xmax": {"name": "xmax", "group": "Ungrouped variables", "definition": "if(a>0,expression('x1'),expression('x2'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "k", "xmin", "xmax"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>L&oslash;s likningen $f(x)=0$ for &aring; finne eventuelle nullpunkter.</p>\n<p>Skriv inn nullpunkter i stigende rekkef&oslash;lge</p>\n<p>$x=$[[0]]&nbsp; &nbsp;$x=$[[1]] &nbsp;&nbsp;$x=$[[2]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-abs({k})", "maxValue": "-abs({k})", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "abs({k})", "maxValue": "abs({k})", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn $f'(x)$</p>", "answer": "3*{a}*x^2-{a*k^2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>L&oslash;s likningen $f'(x)=0$ og finn eventuelle stasjon&aelig;re punkter</p>\n<p>Skriv inn stasjon&aelig;re punkter i stigende rekkef&oslash;lge</p>\n<p>$x_1=$[[0]]&nbsp; &nbsp;$x_2=$[[1]]</p>\n<p>Legg inn punktene i eksakt form, alts&aring; ikke som desimaltall. Husk: For &aring; skrive $\\sqrt{tall}$ skriv sqrt(tall)</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-abs({k})/(sqrt(3))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.001", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "abs({k})/(sqrt(3))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Bruk fortegnsskjema for $f'(x)$ eller andrederiverttesten (finn $f''(x_1)$ og $f''(x_2)$) for &aring; avgj&oslash;re om $x_1$ og $x_2$ i oppgave c) er lokale minimum eller maksimum.</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\var{xmin}$", "$\\var{xmax}$"], "matrix": [["1", 0], [0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["et lokalt minimum", "et lokalt maximum"]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn $f''(x)$</p>", "answer": "6*{a}*x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>L&oslash;s likningen $f''(x)=0$ og bruk fortegnsskjema for &aring; finne eventuelle vendepunkter</p>\n<p>$x=$[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Tegn grafen til $f(x)$ ved &aring; sette inn funksjonsutrykket under, og sammenlign med resultatene du har f&aring;tt i oppgavene a), d), f). Husk &aring; skrive inn := ikke =</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/e5jkajyb')}</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Den deriverte, ekstremalpunkter, monotoniegenskap, krumning (teori)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>La $f(x)$ v&aelig;re deriverbar for alle $x\\in\\mathbb{R}$</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>For hver rad finn passende alternativ</p>\n<p>Merk: Ser du ikke hele tabellen bruk Ctrl og + eller - for &aring; justere st&oslash;rrelsen.</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$f'(a)=0$<br/>_____________________________________________________", "$f'(a)=0$ og $f'(x)$ skifter fortegn fra positiv til negativ i $x=a$<br/>_____________________________________________________", "$f'(a)=0$ og $f'(x)$ skifter fortegn fra negativ til positiv&nbsp;i $x=a$<br/>_____________________________________________________", "$f'(a)=0$ og $f''(a)&gt;0$&nbsp;<br/>_____________________________________________________", "$f'(a)=0$ og $f''(a)&lt;0$&nbsp;<br/>_____________________________________________________", "$f'(x)&lt;0$ for alle $x\\in(a,b)$<br/>_____________________________________________________", "$f'(x)&gt;0$ for alle $x\\in(a,b)$<br/>_____________________________________________________", "$f''(a)=0$ og $f''(x)$ skifter fortegn fra positiv til negativ i $x=a$<br/>_____________________________________________________", "$f''(a)=0$ og $f''(x)$ skifter fortegn fra negativ til positiv i $x=a$<br/>_____________________________________________________", "$f''(x)&lt;0$ for alle $x\\in(a,b)$<br/>_____________________________________________________", "$f''(x)&gt;0$ for alle $x\\in(a,b)$<br/>_____________________________________________________"], "matrix": [["1", 0, 0, 0, 0, 0, 0, 0], [0, "0", "1", 0, 0, 0, 0, 0], [0, "1", "0", 0, 0, 0, 0, 0], [0, "1", 0, "0", 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0], [0, 0, 0, 0, 0, "1", "0", 0], [0, 0, 0, 0, 0, 0, "1", "0"], [0, 0, 0, 0, 0, 0, 0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["$x=a$ er et stasjon&aelig;rt punkt", "$x=a$ er et lokalt minimum", "$x=a$ er et lokalt maksimum", "$f(x)$ er strengt avtakende p&aring; $(a,b)$", "$f(x)$ er strengt voksende p&aring; $(a,b)$", "$x=a$ er et vendepunkt", "$f(x)$ er strengt konkav p&aring; $(a,b)$", "$f(x)$ er strengt konveks p&aring; $(a,b)$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}