Chapter 8.5, Problem 42E

(a)

To determine

If $f\left(3\right)-f\left(2\right)>0$, when $f^{\prime }\left(x\right)=\frac{5x^3+10x}{{\left(x^2+1\right)}^2}$.

(b)

To determine

Whether the area under the graph of $f^{\prime }$ from 1 to 2 is greater than the area under the graph of $f^{\prime }$ from 3 to 4, when $f^{\prime }\left(x\right)=\frac{5x^3+10x}{{\left(x^2+1\right)}^2}$.