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