# Thread: find max slope multivariable

1. ## find max slope multivariable

$\displaystyle z=e^{-(x^2+y^2)}$
find the maximum slope and give answer in degrees

I believe that since this is a paraboloid and is symmetrical that I can treat it with only the z and x axis. So I take the second order partial derivative with respect to x and get
$\displaystyle 4xe^{-(x^2+y^2)}-2e^{-(x^2+y^2)}$ and equate it with 0. After that I have no clue how to proceed.

2. The function $\displaystyle f(x,y)=e^{-(x^2+y^2)}$ is radially symmetric right? We can write it in polar coordinates as $\displaystyle f(r,\theta)=e^{-r^2}$
So first find $\displaystyle f_r$, then find where it has a maximum value. That gives you the r value. But the function is independent of $\displaystyle \theta$ so any $\displaystyle \theta$ with that r will also have a maximum value. So the function will have a maximum slope over a circular region with radius r.

3. I'm sorry but I haven't learned about polar coordinates. I haven't learned about vectors yet either.