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Draw the graph of for . .

  1. Write an equation for .

    Use the product rule.

  2. Graph using your graphing calculator. Then, use this graph to locate the -value of the local maximum of over .

    The location of a local maximum on can be found where AND changes from positive values to negative values.

  3. Likewise, use a graph of to locate the point of inflection of for .

    A zero on the second derivative that crosses the -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