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November 9, 2021

How do relative (or local) minimum points, relative (or local) maximum points, and inflection points affect the shap

Mathematics /Calculus

How do relative (or local) minimum points, relative (or local) maximum points, and inflection points affect the shape of the graph of a given function? That is, why might someone use derivative techniques to find these points before sketching the graph of a function (assuming no graphing calculator)?

How does someone determine the intervals over which a function is increasing or decreasing? What has to be true about the slope of the tangent in each situation (increasing vs. decreasing)?

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