Question

Determine whether Rolle's Theorem can be applied to f(x) = x^4-2x^2, on (-2, 2). If so, find the c that supports the theorem.

I found that Rolle's theorem CAN be applied since f(a) = f(b), but I dont know how to find the c value.

Answer 1

find f'(x)
evaluate f'(x) at x=c
and set f'(c)=0

Answer 2

f'(x)=4x^3-4x
f'(c)=4c^3-4c
4c^3-4c=0 solve for c