Differentiability: Corners, Cusps and Piecewise Functions Worksheet with Answer Key

What's on the worksheet

1. Find $f'_-
   f(x) = |x - 2| + |x + 1|, \; a = -1f(x) = (x - 1)\,|x^2 - 1|, \; a = 1f(x) = |x^3 - 8|, \; a = 2
2. The figure shows the graph of a function g on [-5, 6].
3. Each function is continuous at the given point.
   f(x) = x + \sqrt[3]{x - 2} at x = 2f(x) = \sqrt{x + |x|} at x = 0f(x) = \sqrt[3]{x^3 - x^2} at x = 0
4. Decide whether f is differentiable at the join.
5. Mateo rides an electric tram away from a stop.
6. Find the constants a and b that make f differentiable at every number.