Instructor: Martinez, Juan Spring $2025$

Name $q,$ jeater

ID# $q,$

Show all your work. Each problem is worth $4$pts$.$ Circle $($or box$)$ your ans

Consider the function.

$f(x)=x{e}^{-x}$

a$)$ Find the intervals on which $f$ is increasing or decreasing.

b$)$ Find the local maximum and minimum values of $f.$

c$)$ Find the intervals of concavity and inflection points.

d$)$ Using the above information, sketch the graph of $f.($Label appropr