Determine if the Mean Value Theorem FOR INTEGRALS applies to the function f(x) = x3 − 4x on the interval [−1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem.

Question

THANK YOU VERY MUCH

Answer 1

The MVT applies to all polynomials, since they are continuous and differentiable everywhere.
The slope of the line joining the endpoints of the graph is
(f(1)-f(-1))/(1 - (-1)) = -3
Since f'(x) = 3x^2-4
you want to find the value c such that
3c^2 - 4 = -3

Answer 2

Thank you, but are you doing the MVT for the derivative? Because my question is in terms of integrals, and when I do it for integrals I get a different answer than -3