// Numbas version: exam_results_page_options
{"name": "Slope of a curve at a point", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "extensions": [], "statement": "<p>Calculate the slope of the curve</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=\\var{a}x^3-\\var{b}x^2+\\var{c}x+\\var{d}\\)</p>\n<p>at the point where \\(x=\\var{f}\\).&nbsp;</p>", "parts": [{"prompt": "<p>Input your answer correct to one decimal place.</p>\n<p style=\"padding-left: 30px;\">\\(slope = \\)&nbsp;[[0]]</p>", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "mustBeReduced": false, "precisionPartialCredit": 0, "minValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "customMarkingAlgorithm": "", "allowFractions": false, "marks": 1, "precisionType": "dp", "precision": "1", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "mustBeReducedPC": 0, "unitTests": []}], "variableReplacements": [], "showCorrectAnswer": true, "sortAnswers": false, "unitTests": [], "customMarkingAlgorithm": "", "marks": 0}], "metadata": {"description": "<p>Slope of a curve at a point</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"c": {"description": "", "templateType": "randrange", "name": "c", "definition": "random(5..12#1)", "group": "Ungrouped variables"}, "f": {"description": "", "templateType": "randrange", "name": "f", "definition": "random(0..4#1)", "group": "Ungrouped variables"}, "b": {"description": "", "templateType": "randrange", "name": "b", "definition": "random(2..10#1)", "group": "Ungrouped variables"}, "d": {"description": "", "templateType": "randrange", "name": "d", "definition": "random(10..20#1)", "group": "Ungrouped variables"}, "a": {"description": "", "templateType": "randrange", "name": "a", "definition": "random(2..6#1)", "group": "Ungrouped variables"}}, "ungrouped_variables": ["a", "b", "c", "d", "f"], "advice": "<p>\\(f(x)=\\var{a}x^3-\\var{b}x^2+\\var{c}x+\\var{d}\\)</p>\n<p>The equation for the slope of a curve is found by differentiating the function.</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=3*\\var{a}x^2-2*\\var{b}x+\\var{c}\\)</p>\n<p>To find the slope at a particular point we simply insert the x-coordinate value into this equation.</p>\n<p style=\"padding-left: 30px;\">Slope = \\(3*\\var{a}*\\var{f}^2-2*\\var{b}*\\var{f}+\\var{c}\\)</p>\n<p style=\"padding-left: 30px;\">Slope = \\(\\simplify{3*{a}*{f}^2-2*{b}*{f}+{c}}\\)</p>", "variable_groups": [], "name": "Slope of a curve at a point", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "functions": {}, "rulesets": {}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}