// Numbas version: exam_results_page_options {"name": "Slope of a curve at a point [L7 Random]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f"], "extensions": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "parts": [{"showCorrectAnswer": true, "unitTests": [], "marks": 0, "gaps": [{"showCorrectAnswer": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "precisionType": "dp", "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "minValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "extendBaseMarkingAlgorithm": true, "maxValue": "3*{a}*{f}^2-2*{b}*{f}+{c}", "precision": "1", "showPrecisionHint": false, "marks": 1, "strictPrecision": false, "allowFractions": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "precisionPartialCredit": 0}], "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "

Input your answer correct to one decimal place.

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\\(slope = \\) [[0]]

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\\(f(x)=\\var{a}x^3-\\var{b}x^2+\\var{c}x+\\var{d}\\)

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The equation for the slope of a curve is found by differentiating the function.

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\\(\\frac{df}{dx}=3*\\var{a}x^2-2*\\var{b}x+\\var{c}\\)

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To find the slope at a particular point we simply insert the x-coordinate value into this equation.

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Slope = \\(3*\\var{a}*\\var{f}^2-2*\\var{b}*\\var{f}+\\var{c}\\)

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Slope = \\(\\simplify{3*{a}*{f}^2-2*{b}*{f}+{c}}\\)

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Slope of a curve at a point

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Calculate the slope of the curve

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\\(f(x)=\\var{a}x^3-\\var{b}x^2+\\var{c}x+\\var{d}\\)

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at the point where \\(x=\\var{f}\\). 

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