Question

Determine if the function
f(x) = x^2 − 3x + 1
satisfies the hypotheses of the Mean Value
Theorem (MVT) on the interval [−4, 0].
If it does, find all possible values of c satisfying the conclusion of the MVT

Answer 1

Do you know what the hypotheses is?
It is the if part.
Does it satisfy the if part of the theorem?

Answer 2

What do you think? Is f(x) continuous on the interval (-4, 0)? Is f(x) differentiable on (-4, 0)? Do you have your textbook available so that you could look up the Mean Value Theorem? I have a textbook right here, but would prefer that you identify for yourself what the hypotheses of the Theorem are.