Chapter 4, Problem 51RE

Mean Value Theorem For the function $f\left(x\right)=\sqrt{10x}$ and the interval [a, b] = [0, 10], use the graph to make a conjecture about the value of c for which $\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{\prime }\left(c\right)$. Then verify your conjectured value by solving the equation $\frac{f\left(b\right)-f\left(a\right)}{b-a}=f^{\prime }\left(c\right)$ for c.