(a) Use a computer algebra system to find an antiderivative $F$ of $$f(x)=\frac{x^2-1}{x^4+x^2+1}$$ such that $F(0)=0.$

$f(x) =$

(b) Use the graphs of $f$ and $F$ to locate approximately the $x$-coordinates of the extreme points. List the extreme points in increasing order, and state whether they are a local maximum or minimum in the appropriate place. If any blanks are unused, type "N" in each one and designate the type of point as "unused".

Smallest extreme point: $x =$

? Minimum Maximum Unused  1. Minimum or maximum?

Next smallest extreme point: $x =$

? Minimum Maximum Unused  1. Minimum or maximum?

Next smallest extreme point: $x =$

? Minimum Maximum Unused  1. Minimum or maximum?

Next smallest extreme point: $x =$

? Minimum Maximum Unused  1. Minimum or maximum?

(c) Use the graphs of $f$ and $F$ to locate approximately the $x$-coordinates of the inflection points. List the inflection points in increasing order. If any blanks are unused, type "N" in each one.

Smallest inflection point: $x =$

Next smallest inflection point: $x =$

Next smallest inflection point: $x =$

Next smallest inflection point: $x =$