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[Solution Library] Prove that the function f(x)=x^2/3 doesn’t satisfy the hypothesis of the mean value theorem on [-1, 27], but that nevertheless there is a number

Question: Prove that the function $f\left( x \right)={{x}^{2/3}}$ doesn’t satisfy the hypothesis of the mean value theorem on [-1, 27], but that nevertheless there is a number c in (-1, 27) such that

\[f'\left( c \right)=\frac{f\left( 27 \right)-f\left( -1 \right)}{27-\left( -1 \right)}\]

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[Solution Library] Prove that the function f(x)=x^2/3 doesn’t satisfy the hypothesis of the mean value theorem on [-1, 27], but that nevertheless there is a number

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