Chapter 4.3, Problem 4E

Let $g\left(x\right)={\displaystyle {\int }_0^{x}f\left(t\right)dt}$ where f is the function whose graph is shown.

(a) Evaluate $g\left(0\right)$ and $g\left(6\right)$.

(b) Estimate $g\left(x\right)$ for $x=1,2,3,4,\text{ and 5}$.

(c) On what interval is g increasing?

(d) Where does g have a maximum value?

(e) Sketch a rough graph of g.

(f) Use the graph in part (e) to sketch the graph of $g\prime \left(x\right)$. Compare with the graph of f.