Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)

Question

f(x) = x^3 − x^2 − 12x + 8, [0, 4]

Answer 1

f is a polynomial, so it is continuous and differentiable

f(4) = f(0) = 8, so that's ok

So, you want c where f'(c) = 0
That means you need

3c^2 - 2c - 12 = 0
c = 2.361
The other value is not in [0,4]