Chapter 2.3, Problem 50E

(a) Graph the function $g\left(x\right)=x^2/\left(x^2+1\right)$ in the viewing rectangle $\left[-4,4\right]$ by $\left[-1,1.5\right]$.

(b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of $g\text{'}$. (See Example 2.2.1.)

(c) Calculate $g\text{'}\left(x\right)$ and use this expression, with a graphing device, to graph $g\text{'}$. Compare with your sketch in part (b).