Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.
-$f ( x ) = x ^ { 1 / 3 }$

Name: Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -$f ( x ) = x ^ { 1 / 3 }$
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Question

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The function $f(x) = x^{1/3}$ is continuous on any interval in $\mathbb{R}$, but it is not differentiable at $x = 0$, which violates one of the hypotheses of the Mean Value Theorem.

Determine Whether the Function Satisfies the Hypotheses of the Mean f(x)=x1/3f ( x ) = x ^ { 1 / 3 }f(x)=x1/3

Determine Whether the Function Satisfies the Hypotheses of the Mean $f ( x ) = x ^ { 1 / 3 }$