// Numbas version: finer_feedback_settings
{"name": "Ida's copy of Applications of differentiation ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p><strong>Parts A and B</strong></p>\n<p>Here, the question takes you throught the stages needed to find the solution. The reason we differentiate is that the derivative of a function tells us its gradient at a given point, and we want to find where the function has gradient zero because when the gradient is zero we either have a maximum or a minimum point.</p>\n<p><strong>Part C</strong></p>\n<p>The first part of this question is similar to parts A and B. The tricky bit is the second part! You need to work out the value of $t$ that produces the maximum piont but that is not the final answer - you need to use that value of $t$ to find the maximum height, which you do by substituting $t$ into the original function to find $y$.</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "statement": "<p>Finn vendepunktet til funksjonen $y=\\simplify {{f}x^2+{g}x+{h}}$. Oppgi svaret med $2$ desimalers n&oslash;yaktighet.&nbsp;</p>\n<p>Bestem om punktet er et maksimalpunkt eller et minimalpunkt.&nbsp;</p>", "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "tags": [], "parts": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "gaps": [{"showFeedbackIcon": true, "variableReplacements": [], "maxValue": "-g/(2*f)", "type": "numberentry", "minValue": "-g/(2*f)", "mustBeReducedPC": 0, "strictPrecision": false, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReduced": false, "precision": "2", "variableReplacementStrategy": "originalfirst", "scripts": {}, "precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "correctAnswerFraction": false, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false, "precisionPartialCredit": 0}, {"showFeedbackIcon": true, "variableReplacements": [], "maxValue": "g^2/(4*f)-g^2/(2*f)+h", "type": "numberentry", "minValue": "g^2/(4*f)-g^2/(2*f)+h", "mustBeReducedPC": 0, "strictPrecision": false, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReduced": false, "precision": "2", "variableReplacementStrategy": "originalfirst", "scripts": {}, "precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "correctAnswerFraction": false, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false, "precisionPartialCredit": 0}, {"showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "expectedvariablenames": [], "type": "jme", "showpreview": true, "vsetrangepoints": 5, "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "scripts": {}, "answer": "2*{f}*x+{g}", "marks": 1, "checkingaccuracy": 0.001, "checkingtype": "absdiff"}, {"showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "expectedvariablenames": [], "type": "jme", "showpreview": true, "vsetrangepoints": 5, "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "scripts": {}, "answer": "2*{f}", "marks": 1, "checkingaccuracy": 0.001, "checkingtype": "absdiff"}, {"showFeedbackIcon": true, "variableReplacements": [], "shuffleChoices": false, "displayType": "radiogroup", "distractors": ["", ""], "type": "1_n_2", "showCorrectAnswer": true, "choices": ["<p>maximalpunkt</p>", "<p>minimalpunkt</p>"], "variableReplacementStrategy": "originalfirst", "scripts": {}, "matrix": ["if(maximum, 1, 0)", "if(maximum, 0, 1)"], "maxMarks": "0", "displayColumns": 0, "marks": 0, "minMarks": 0}], "type": "gapfill", "marks": 0, "prompt": "<p></p>\n<p>Regn f&oslash;rst ut den deriverte og den andrederiverte.</p>\n<p></p>\n<p>$\\displaystyle \\frac{dy}{dx}=$&nbsp;[[2]]</p>\n<p>$\\displaystyle \\frac{d^2y}{dx^2}=$&nbsp;[[3]]</p>\n<p></p>\n<p>Dernest, finn $x$ slik at $\\displaystyle \\frac{dy}{dx}=0$.</p>\n<p>$x$-koordinaten til vendepunktet er $=$&nbsp;[[0]]</p>\n<p>Vendepunktet er et&nbsp;&nbsp;[[4]]</p>\n<p></p>\n<p></p>", "showCorrectAnswer": true, "variableReplacements": []}], "extensions": [], "variables": {"a": {"definition": "random(0..10#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "name": "a"}, "w": {"definition": "random(2..5#0.1)", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "name": "w"}, "b": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "b"}, "maximum": {"definition": "f<0", "templateType": "anything", "group": "Ungrouped variables", "description": "<p>Is the stationary point a maximum?</p>", "name": "maximum"}, "z": {"definition": "random(20..30#0.5)", "templateType": "randrange", "group": "Ungrouped variables", 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