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Given: where and are constants. 

  1. For what value(s) of is the graph non-differentiable, regardless of the values of and ? Explain what happens to at these points.

    has a cusp within the domain of one of the pieces. Where is it?

  2. Find values of and so the graph is both continuous and differentiable at .

    Write a system of equations: [piece of ] [piece of ], evaluated at . [piece of ] [piece of ], evaluated at .
    Use algebra to solve for and .

Use the eTool below to visualize the problem.
Click the link at right for the full version of the eTool: Calc 6-29 HW eTool