f(x) = 1 − x2/3 Find f(−1) and f(1).

Question

Consider the following function.

f(x) = 1 − x^2/3

Find f(−1) and f(1).

f(−1)	=
f(1)	=

Find all values c in (−1, 1) such that f '(c) = 0.

 (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

c = 

 

Based off of this information, what conclusions can be made about Rolle's Theorem?

This contradicts Rolle's Theorem, since f is differentiable, f(−1) = f(1), and f '(c) = 0 exists, but c is not in (−1,

This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−1, 1).    

This contradicts Rolle's Theorem, since f(−1) = f(1), there should exist a number c in (−1, 1) such that f '(c) = 0.

This does not contradict Rolle's Theorem, since f '(0) does not exist, and so f is not differentiable on (−1, 1).

Nothing can be concluded.

Answer 1

f(1)=f(-1)=0

f' ≠ 0 anywhere

f is continuous at 0 but not differentiable at 0

Rolle's theorem does not apply