Question

Rolle's theorem cannot be applied to the function f(x) = x1/3 on the interval [–1, 1] because

Answer Choices:

f is not differentiable on the interval [–1, 1]

f(–1) ≠ f(1)

f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1)

Rolle's theorem can be applied to f(x) = x1/3 on the interval [–1, 1]

Answer 1

Check the graph. Is f'(x)=0 anywhere on the interval?

Clearly not, so now you have to figure out why.

Is f(-1) = f(1)?

Is df/dx defined everywhere on the interval? (check out x=0)