// 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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "extensions": [], "statement": "

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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Input your answer correct to one decimal place.

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\$$slope = \$$ [[0]]

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Slope of a curve at a point

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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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