// Numbas version: finer_feedback_settings
{"name": "Bestimmung eines Flachpunkts", "extensions": [], "custom_part_types": [], "resources": [["question-resources/funktion.png", "funktion.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Bestimmung eines Flachpunkts", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Gegeben sei $ f(x) = \\frac{1}{3} x^3 - 4x + 1 $ als Funktionsterm der Funktion $ f $.</p>\n<p><img src=\"resources/question-resources/funktion.png\"/></p>", "advice": "<p>&Auml;ndert die zweite Ableitung an einem Punkt das Vorzeichen, so liegt ein Wendepunkt vor.</p>\n<p>Bleibt es gleich, so handelt es sich um einen Flachpunkt.</p>", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Wie lautet die erste Ableitung der Funktion $ f $ nach $ x $? (Hinweis: Verwende das \"^\"-Zeichen zur Eingabe von Exponenten wie in \"<em>x^2</em>\")</p>", "answer": "x^2-4", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "gapfill", "useCustomName": true, "customName": "b)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: left;\">An welchen Stellen nimmt die Funktion $ f $ lokale Extrema ein?</p>\n<p></p>\n<ul>\n<li>lokales Maximum bei&nbsp; $ x = $&nbsp; [[0]]</li>\n</ul>\n<p></p>\n<ul>\n<li>lokales Minimum bei&nbsp;&nbsp; $ x = $&nbsp; [[1]]</li>\n</ul>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Maximum", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-2", "maxValue": "-2", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["si-fr", "eu", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": true, "customName": "Minimum", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "2", "maxValue": "2", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["si-fr", "eu", "plain-eu"], "correctAnswerStyle": "si-fr"}], "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>Wie lautet die zweite Ableitung $ f''(x) $?</p>", "answer": "2x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "1_n_2", "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>Liegt f&uuml;r $ x = 0 $ nur ein Flach- oder auch Wendepunkt vor?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["nur ein Flachpunkt, aber kein Wendepunkt", "ein Wendepunkt"], "matrix": [0, "1"], "distractors": ["", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Tobias Ruff", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2314/"}], "resources": ["question-resources/funktion.png"]}]}], "contributors": [{"name": "Tobias Ruff", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2314/"}]}