2. Intro to Derivatives

b. Show that

f(x) = { x² sin(1/x), x ≠ 0

0, x = 0

is differentiable at x = 0 and find f′(0).

Theory and Examples

In Exercises 51 and 52, give reasons for your answers.

Let f(x) = |x³ − 9x|.

a. Does f'(0) exist?