// Numbas version: exam_results_page_options
{"name": "Derivatives from first principles, quadratic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Derivatives from first principles, quadratic", "tags": [], "metadata": {"description": "<p>Derivatives from first principles, quadratic</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<h3><strong>Finding a derivative from the definition of a derivative:</strong></h3>\n<p><strong>Definition:</strong> The derivative of \\(f(x)\\) with respect to \\(x\\) is the function \\(f'(x)\\) defined as \\[f'(x)=\\lim_{h\\rightarrow0}\\frac{f(x+h)-f(x)}{h}\\]</p>", "advice": "<p>Reveal the steps.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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><strong>Reveal the steps for a step-by-step procedure:</strong></p>\n<p>Given \\[f(x)=\\simplify{{substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"a*x^2+b*x+c\"))}}\\]find \\(f'(x)\\), without using the rules for differentiation, but using the definition above.</p>", "stepsPenalty": 0, "steps": [{"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>Let \\(h&gt;0\\) be a parameter. The slope of the secant line through \\((x,f(x))\\) and \\((x+h,f(x+h))\\) is \\[\\frac{f(x+h)-f(x)}{h}\\]</p>\n<p>Using the functional form find the value \\(f(x)\\)&nbsp;</p>", "answer": "{substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"a*x^2+b*x+c\"))}", "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, "prompt": "<p>Find the value of \\(f(x+h)\\)&nbsp;</p>", "answer": "{substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"a*(x+h)^2+b*(x+h)+c\"))}", "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, "prompt": "<p>Substitute the above and find the value of \\[\\frac{f(x+h)-f(x)}{h}\\]</p>", "answer": "{substitute([\"a\":a,\"b\":b],expression(\"(a*(2*h*x+h^2)+b*h)/h\"))}", "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": "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>Finally, find \\[\\lim_{h\\rightarrow0}\\frac{f(x+h)-f(x)}{h}\\]</p>"}], "answer": "{substitute([\"a\":a,\"b\":b,\"c\":c],expression(\"2*a*x+b\"))}", "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": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Emil Kostadinov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/10391/"}]}]}], "contributors": [{"name": "Emil Kostadinov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/10391/"}]}