Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.
-$g ( x ) = x ^ { 3 / 4 }$ , $[0,5]$

Question

Quizplus · Accepted Answer

For the function to satisfy the hypotheses of the Mean Value Theorem, it should be continuous on the closed interval $[0,5]$ and differentiable on the open interval $(0,5)$.

In this case, $g(x) = x^{3/4}$ is continuous on $[0,5]$ since it is a polynomial function. Also, it is differentiable on $(0,5)$ since its derivative $g'(x) = \frac{3}{4}x^{-1/4}$ exists on this interval.

Therefore, the function satisfies the hypotheses of the Mean Value Theorem.

Determine Whether the Function Satisfies the Hypotheses of the Mean g(x)=x3/4g ( x ) = x ^ { 3 / 4 }g(x)=x3/4

Determine Whether the Function Satisfies the Hypotheses of the Mean $g ( x ) = x ^ { 3 / 4 }$