// Numbas version: exam_results_page_options
{"name": "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": [{"rulesets": {"std": ["all", "fractionNumbers", "!noLeadingMinus", "!collectNumbers"]}, "variable_groups": [], "tags": [], "parts": [{"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "useCustomName": false, "marks": 1, "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "vsetRange": [0, 1], "showCorrectAnswer": true, "type": "jme", "showPreview": true, "valuegenerators": [], "checkVariableNames": false, "failureRate": 1, "answerSimplification": "std", "customName": "", "scripts": {}, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "answer": "{a} - {root}"}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "useCustomName": false, "marks": 1, "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "vsetRange": [0, 1], "showCorrectAnswer": true, "type": "jme", "showPreview": true, "valuegenerators": [], "checkVariableNames": false, "failureRate": 1, "answerSimplification": "std", "customName": "", "scripts": {}, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "answer": "{a} + {root}"}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "useCustomName": false, "marks": "1", "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "vsetRange": [0, 1], "showCorrectAnswer": true, "type": "jme", "showPreview": true, "valuegenerators": [{"name": "x", "value": ""}], "checkVariableNames": false, "failureRate": 1, "answerSimplification": "all", "customName": "", "scripts": {}, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "answer": "(({a} -{b})^2 + {c} - (x -{a})^2)/((x - {b})^2 + {c})^2"}], "unitTests": [], "type": "gapfill", "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>"}], "functions": {}, "name": "Stationary points of rational functions", "ungrouped_variables": ["a", "c", "b", "root"], "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Finding the stationary points of a&nbsp;rational function with specific features.</p>"}, "extensions": [], "statement": "<p><strong>Locate&nbsp;the stationary points of the function.</strong></p>", "advice": "", "variables": {"c": {"description": "", "definition": "random(1.. 7)", "group": "Ungrouped variables", "name": "c", "templateType": "anything"}, "b": {"description": "", "definition": "random(-5..5)", "group": "Ungrouped variables", "name": "b", "templateType": "anything"}, "root": {"description": "", "definition": "sqrt((a - b)^2 + c)", "group": "Ungrouped variables", "name": "root", "templateType": "anything"}, "a": {"description": "", "definition": "random(-5..5)", "group": "Ungrouped variables", "name": "a", "templateType": "anything"}}, "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": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Ian Davies", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3119/"}]}]}], "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": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Ian Davies", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3119/"}]}