// Numbas version: exam_results_page_options
{"name": "Praneetha's copy of 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": [{"variable_groups": [], "variables": {"c": {"description": "", "definition": "random(5..12#1)", "templateType": "randrange", "name": "c", "group": "Ungrouped variables"}, "a": {"description": "", "definition": "random(2..6#1)", "templateType": "randrange", "name": "a", "group": "Ungrouped variables"}, "d": {"description": "", "definition": "random(10..20#1)", "templateType": "randrange", "name": "d", "group": "Ungrouped variables"}, "b": {"description": "", "definition": "random(2..10#1)", "templateType": "randrange", "name": "b", "group": "Ungrouped variables"}, "f": {"description": "", "definition": "random(0..4#1)", "templateType": "randrange", "name": "f", "group": "Ungrouped variables"}}, "functions": {}, "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>", "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>", "metadata": {"description": "<p>Slope of a curve at a point</p>", "licence": "Creative Commons Attribution 4.0 International"}, "tags": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "extensions": [], "ungrouped_variables": ["a", "b", "c", "d", "f"], "name": "Praneetha's copy of Slope of a curve at a point", "parts": [{"scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "gaps": [{"scripts": {}, "showCorrectAnswer": true, "precision": "1", "type": "numberentry", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "marks": 1, "precisionType": "dp", "maxValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "precisionPartialCredit": 0, "allowFractions": false, "minValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false}], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p>Input your answer correct to one decimal place.</p>\n<p style=\"padding-left: 30px;\">\\(slope = \\)&nbsp;[[0]]</p>", "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Praneetha Singh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2552/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Praneetha Singh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2552/"}]}