Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.
-$f ( x ) = x ^ { 1 / 3 }$ , $[-5,2]$

Question

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The function $f(x) = x^{1/3}$ is continuous on the closed interval $[-5,2]$ but not differentiable at $x=0$, which violates one of the Mean Value Theorem's hypotheses that the function must be differentiable on the open interval $(-5,2)$.

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 $f ( x ) = x ^ { 1 / 3 }$