Chapter 4, Problem 59RE

Let $f\left(x\right)=\frac{x^3+2}{x^4+1}$

(a) Generate the graph of $y=f\left(x\right),$ and use the graph to make rough estimates of the coordinates of the absolute extrema.

(b) Use a CAS to solve the equation $f^{\prime }\left(x\right)=0$ and then use it to make more accurate approximations of the coordinates in part (a).