Determine whether Rolle's Theorem can be applied to f on the interval. (Select all that apply.)

Question

f(x)=|x|-2, [-2,2]

a) Yes, Rolle's Theorem can be applied.

b) No, because f is not continuous on the closed interval [a, b].

c) No, because f is not differentiable in the open interval (a, b).

d) No, because f(a) ≠ f(b).

c= ?

I thought it was b) but I got it wrong

Answer 1

It's continuos. It's just that with absolute value functions they have a sharp point that have infinite slopes. In order to be differentiable the functions have to be 'smooth'. The function is not differentiable a x = 0.

It's probably c. Answer d is that supposed to be f of a = f prime of b?... that seems irrelevant.