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{"name": "Maria's copy of Stationary points of rational functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"unitTests": [], "showCorrectAnswer": true, "prompt": "<p>$f(x)=\\simplify[all,!collectNumbers]{(x -{a})/((x -{b})^2 + {c}) }$</p>\n<p>$f'(x)=$&nbsp;[[2]]</p>\n<p></p>\n<p>Find when $f'(x)=0$, hence find:</p>\n<p>$x$-coordinate of the stationary point giving a minimum $=$&nbsp;[[0]]</p>\n<p>$x$-coordinate of the stationary point giving a maximum $=$&nbsp;[[1]]</p>", "extendBaseMarkingAlgorithm": true, "gaps": [{"unitTests": [], "checkingAccuracy": 0.001, "showPreview": true, "expectedVariableNames": [], "failureRate": 1, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "answerSimplification": "std", "vsetRangePoints": 5, "checkVariableNames": false, "checkingType": "absdiff", "type": "jme", "answer": "{a} - {root}", "showCorrectAnswer": true, "marks": 1, "scripts": {}}, {"unitTests": [], "checkingAccuracy": 0.001, "showPreview": true, "expectedVariableNames": [], "failureRate": 1, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "answerSimplification": "std", "vsetRangePoints": 5, "checkVariableNames": false, "checkingType": "absdiff", "type": "jme", "answer": "{a} + {root}", "showCorrectAnswer": true, "marks": 1, "scripts": {}}, {"unitTests": [], "checkingAccuracy": 0.001, "showPreview": true, "expectedVariableNames": [], "failureRate": 1, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "answerSimplification": "all", "vsetRangePoints": 5, "checkVariableNames": false, "checkingType": "absdiff", "type": "jme", "answer": "(({a} -{b})^2 + {c} - (x -{a})^2)/((x - {b})^2 + {c})^2", "showCorrectAnswer": true, "marks": "1", "scripts": {}}], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "scripts": {}}], "advice": "", "ungrouped_variables": ["a", "c", "b", "root"], "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Finding the stationary points of a&nbsp;rational function with specific features.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p><strong>Locate&nbsp;the stationary points of the function.</strong></p>", "name": "Maria's copy of Stationary points of rational functions", "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"c": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1.. 7)", "name": "c"}, "root": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "sqrt((a - b)^2 + c)", "name": "root"}, "a": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-5..5)", "name": "a"}, "b": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-5..5)", "name": "b"}}, "variable_groups": [], "extensions": [], "rulesets": {"std": ["all", "fractionNumbers", "!noLeadingMinus", "!collectNumbers"]}, "type": "question", "contributors": [{"name": "cormac breen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/306/"}, {"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Ian Davies", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3119/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "cormac breen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/306/"}, {"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Ian Davies", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3119/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}