The Building Block of Calculus - Chapter 3 Curve Sketching
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Curve sketching involves analyzing functions and determining important features like intercepts, maxima, minima and intervals of increase and decrease to sketch the general shape of the graph without calculating a large number of points. The key steps are to determine the domain, find any vertical, horizontal and oblique asymptotes, analyze the end behavior, locate x-intercepts and any other intercepts with other axes, analyze the first and second derivatives to find critical points and intervals of increase and decrease, and finally sketch the curve combining all this information.
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