Chapter 4.8, Problem 18ES

Review Formulas (6) and (7) in Section 2.1 and use the Mean-Value Theorem to show that if $f$ is differentiable on $\left(-\infty ,+\infty \right),$ then for any interval $\left[x_0,x_1\right]$ there is at least one point in $\left(x_0,x_1\right)$ where the instantaneous rate of change of $y$ with respect to $x$ is equal to the average rate of change over the interval.