Answer
The Mean Value Theorem does not apply to this function because this function is not differentiable on the open interval $(1, 6)$.
Work Step by Step
The Mean Value Theorem requires that this function must be continuous on the closed interval $[1, 6]$ and differentiable on the open interval $(1, 6)$. This function does not satisfy the second condition because this function has a cusp, which is not differentiable, at $x = 3$, which is in the open interval $(1, 6)$. Therefore, the Mean Value Theorem does not apply to this function.
