Answer
$f(x)$ satisfies the hypotheses
(see below for reasons)
Work Step by Step
The two hypotheses of the Mean Value Theorem are:
(1) $y=f(x)$ is continuous over a closed interval $[a, b]$ and
(2) $y$ is differentiable on the interval's interior $(a, b)$ .
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In this problem,
(1) $f(x)$ is continuous over $[0,1]$ due to Th.8. (properties of continuous functions, sec. 2.5)
(2) $f(x)$ is differentiable on $(0,1)$
due to the Power Rule (general version, sec.3.3)
Thus, $f(x)$ satisfies the hypotheses.
