- #1

NanaToru

- 24

- 0

## Homework Statement

Let f(x) = 1 - x

^{2/3}. Show that f(-1) = f(1) but there is no number c in (-1,1) such that f'(c) = 0. Why does this not contradict Rolle's Theorem?

## Homework Equations

## The Attempt at a Solution

f(x) = 1 - x

^{2/3}.

f(-1) = 1 - 1 = 0

f(1) = 1 - 1 = 0

f' = 2/3 x

^{-1/3}.

I don't understand why this doesn't have a number c in f'(c), or why Rolle's theorem excludes nondifferentiable points?