All, you need to do is to check if the function agrees on the end points of the intervals already given to you and proceed to find $c$ asserted to exist by Rolle's Theorem. When you're asked to use Rolle's theorem, you need not find values such that $f(\cdot_1)=f(\cdot_2)$. All you need to do is to verify that the continuity and differentiability hypotheses are true and proceed to find $c$ that is supposed to exist by MVT. So, when you are asked to use Mean value theorem, you don't need to find values such that $f(\cdot_1)=f(\cdot_2)$. $\underline$ there exists a point $c$ in $(a, b)$ such that $$f\ '(c) = 0$$ ![]() differentiable on the open interval $(a, b)$,. ![]()
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