For what value(s) of
is the graph non-differentiable, regardless of the values of and ? Explain what happens to the graph at these points. has a cusp within the domain of one of the pieces. Where is it?
Determine the values of a and
such that the graph is both continuous and differentiable at .
Write a system of equations: [piece 1 of f(x)] = [piece 2 of f(x)], evaluated at
. [piece 1 of f '(x)] = [piece 2 of f '(x)], evaluated at .
Use algebra to solve for
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