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8-88.

GraphLet g(x) = where is shown at right. Homework Help ✎

  1. Evaluate and .

  2. Is ?

    Consider the symmetry of between and .

  3. Express in terms of .

    What is ? What is ?

  4. Is g differentiable over the interval ? Explain.

    Points of NON-differentiablity include cusps, endpoints, jumps, holes, and vertical tangents.

  5. Determine all values of in the interval where has a relative maximum.

    Recall that a local maximum exists where the derivative changes from positive to negative. This can happen where or where .

    Notice that ; after all, the derivative of an integral is the original function.

  6. Write the equation of the line tangent to at .

    What is the slope of  at (see second hint in part (e))? What is the -value?

  7. Determine all values of in the interval where has a point of inflection.

    Concavity is the slope of the slope. So inflection points are where the slope of the slope changes.