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6-29.

f(x) has a cusp within the domain of one of the pieces. Where is it?

Write a system of equations: [piece 1 of f(x)] = [piece 2 of f(x)], evaluated at x = 1. [piece 1 of f '(x)] = [piece 2 of f '(x)], evaluated at x = 1.
Use algebra to solve for a and b.

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