### Home > CALC > Chapter 6 > Lesson 6.1.2 > Problem 6-29

6-29.

Given:

where *a*and*b*are constants. Homework Help ✎For what value(s) of

*x*is the graph non-differentiable, regardless of the values of*a*and*b*? Explain what happens to*f*(*x*) at these points.Find values of

*a*and*b*so the graph is both continuous and differentiable at*x*= 1.

*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