calculus help please!!?

Question

Verify that the function
f(x)=2 x^4 + 2 on [-3, 1]
satisfies the hypotheses of the MVT on the given interval [a, b]. Then find a number c between a and b for which
{f(b)-f(a)} / {(b-a)} = f '(c) .

answer C=__?

Answer 1

f(x) = 2x^4 + 2
f(1) = 4
f(-3) = 20
{f(b)-f(a)} / {(b-a)} = (4 - 20)/(1 + 3) = -4
f'(x) = 8x
f'(c) = 8c = -4
c = -1/2