Homework $9$: Problem $4$

$(15$ points$)$

Let $f(x,y)=x{e}^{x^2-y}$ and $P=(2,4).$

$($a$)$ Calculate $||grad{f}_P||.$

$($b$)$ Find the rate of change of $f$ in the direction $grad{f}_P.$

$($c$)$ Find the rate of change of $f$ in the direction of a vector making an angle of $45$ with $grad{f}_P.$

Answers :

$($a$)$

$($b$)$

$($c$)$

Note: You can earn partial credit on this problem.