// Numbas version: finer_feedback_settings
{"name": "Stasjonaere punkter 2 (kap 7 Sinus)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "r1", "r2", "an", "d", "ap", "xmin", "xmax"], "name": "Stasjonaere punkter 2 (kap 7 Sinus)", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {"std": ["all", "fractionNumbers", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$f(x)=\\simplify[all,!collectNumbers,!noleadingminus, fractionNumbers]{{a}x^3+{b}x^2-{c}x+{d}}$</p>\n<p>$f'(x)=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Bruk blant annet derivasjonsregelen $(x^n )'=n x^{n-1}$</p>\n<p>Videoen i <a href=\"https://www.educreations.com/lesson/view/eksempler-paa-derivasjon-av-polynomfunksjoner/25250346/?ref=link\">denne lenken</a>&nbsp;viser et eksempel p&aring; derivasjon av en polynomfunksjon.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "3*{a}x^2+2*{b}x-{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Unders&oslash;k hvor &nbsp;$f'(x)$ skifter fortegn, og bestem eventuelle topp- og bunnpunkter:</p>\n<p>Koordinatene til bunnpunktet er: (&nbsp;[[0]] ,&nbsp;[[2]] )</p>\n<p>Koordinatene til toppunktet er: (&nbsp;[[1]] ,&nbsp;[[3]] )</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>N&aring;r vi deriverer f&aring;r vi&nbsp;$\\displaystyle f'(x)=\\simplify[std]{{3*a}x^2+{2*b}x-{c}}$.</p>\n<p>For &aring; finne de stasjon&aelig;re punktene m&aring; vi l&oslash;se &nbsp;$\\displaystyle f'(x)=0$&nbsp;for $x$, dvs likningen</p>\n<p>$\\simplify[std]{{3*a}x^2+{2*b}x-{c}=0}$.</p>\n<p>Denne likningen har to l&oslash;sninger; $x=\\var{r1}$ og $x=-\\var{r2}$. For klassifisere de stasjon&aelig;re punktene (avgj&oslash;re om de er toppunkt, bunnpunkt eller terrassepunkt) kan vi tegne fortegnslinja til den deriverte. &nbsp;</p>\n<p>Dere kan finne mer hjelp i denne videosnutten:</p>\n<p><iframe width=\"480\" height=\"300\" frameborder=\"0\" src=\"https://www.educreations.com/lesson/embed/25596966/?s=om0rc2&amp;ref=embed\" allowfullscreen=\"allowfullscreen\"></iframe></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "xmin", "minValue": "xmin", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "xmax", "minValue": "xmax", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "a*xmin^3+b*xmin^2-c*xmin+d", "minValue": "a*xmin^3+b*xmin^2-c*xmin+d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "a*xmax^3+b*xmax^2-c*xmax+d", "minValue": "a*xmax^3+b*xmax^2-c*xmax+d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Her skal vi finne koordinatene til funksjonens stasjon&aelig;re punkter, og avgj&oslash;re om de er toppunkter, bunnpunkter eller terrassepunkter.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-2..2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "3*a*r1*r2", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "3*a*(r2-r1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "r1": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "r1", "description": ""}, "r2": {"definition": "random(1..4 except r1)", "templateType": "anything", "group": "Ungrouped variables", "name": "r2", "description": ""}, "an": {"definition": "if(a<0,1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "an", "description": ""}, "ap": {"definition": "if(a<0,0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ap", "description": ""}, "xmax": {"definition": "an*r1-ap*r2", "templateType": "anything", "group": "Ungrouped variables", "name": "xmax", "description": ""}, "xmin": {"definition": "-an*r2+ap*r1", "templateType": "anything", "group": "Ungrouped variables", "name": "xmin", "description": ""}, "d": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Finding the stationary points of a cubic with two turning points</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}]}]}], "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}]}