// Numbas version: finer_feedback_settings
{"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": [{"tags": [], "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "unitTests": [], "prompt": "<p>Input your answer correct to one decimal place.</p>\n<p style=\"padding-left: 30px;\">\\(gradient = \\)&nbsp;[[0]]</p>", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": false, "correctAnswerFraction": false, "minValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "precisionPartialCredit": 0, "type": "numberentry", "precisionType": "dp", "variableReplacements": [], "scripts": {}, "marks": "2", "unitTests": [], "precision": "1", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "maxValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReduced": false, "allowFractions": false}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Slope of a curve at a point</p>"}, "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d", "f"], "statement": "<p>Calculate the gradient 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>", "functions": {}, "preamble": {"css": "", "js": ""}, "variables": {"c": {"group": "Ungrouped variables", "description": "", "definition": "random(5..12#1)", "name": "c", "templateType": "randrange"}, "f": {"group": "Ungrouped variables", "description": "", "definition": "random(0..4#1)", "name": "f", "templateType": "randrange"}, "b": {"group": "Ungrouped variables", "description": "", "definition": "random(2..10#1)", "name": "b", "templateType": "randrange"}, "a": {"group": "Ungrouped variables", "description": "", "definition": "random(2..6#1)", "name": "a", "templateType": "randrange"}, "d": {"group": "Ungrouped variables", "description": "", "definition": "random(10..20#1)", "name": "d", "templateType": "randrange"}}, "type": "question", "rulesets": {}, "advice": "<p>\\(f(x)=\\var{a}x^3-\\var{b}x^2+\\var{c}x+\\var{d}\\)</p>\n<p>The equation for the gradient 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 gradient 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>", "extensions": [], "name": "Slope of a curve at a point", "variablesTest": {"condition": "", "maxRuns": 100}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}