(a) Use a computer algebra system to find an antiderivative $F$ of $$f(x)=xe^{-x}\sin(x),\quad -5 \le x \le 5,$$ 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 (to at least one decimal place) 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: $x =$