Question

Determine whether the Mean Value Theorem can be applied to f(x)=x^4-8x on [0,2]. If so, find all values of c in (0,2) such that f'(c)=[f(b)-f(a)]/(b-a). if not explain why not.

Answer 1

f(x) is continuous on [0,2] and differentiable on (0,2) so yes

Answer 2

how can you tell?

Answer 3

\(x^4-8x\) is a polynomial. Every polynomial is continuous and has continuous derivatives.

Answer 4

thanks!