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The location of a local maximum on f(x) can be found where f '(x) = 0 AND changes from positive values to negative values.

A zero on the second derivative that crosses the x-axis (or changes sign) indicates a point of inflection on the original function.

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: Calc 5-55 HW eTool