Chapter 2, Problem 27RE

Let $f\left(x\right)=x^2$ . Show that for any distinct values of $a$ and $b$ , the slope of the tangent line to $y=f\left(x\right)$ at $x=\frac{1}{2}\left(a+b\right)$ is equal to the slope of the secant line through the points $\left(a,a^2\right)$ and $\left(b,b^2\right)$ . Draw a picture to illustrate this result.