Chapter 5.8, Problem 2ES

(a) Find $f_{\text{ave}}$ of $f\left(x\right)=x^2$ over $\left[0,2\right]$ .

(b) Find a point $x^{*}$ in $\left[0,2\right]$ such that $f\left(x^{*}\right)=f_{\text{ave}}$ .

(c) Sketch a graph of $f\left(x\right)=x^2$ over $\left[0,2\right]$ , and construct a rectangle over the interval whose area is the same as the area under the graph of $f$ over the interval.