Question

find all the critical points of the function

f(x,y)=(x^2 -3xy+y^2 )e^-(x^2+y^2)

* i got for d/dx=(2x - 3y) e^-(x^2+y^2) +(x^2 - 3 x y + y^2 ) e^-(x^2+y^2) (-2x)
* i got for d/dy=(2y - 3x) e^-(x^2+y^2) +(x^2 - 3 x y + y^2 ) e^-(x^2+y^2) (-2y)

i can't figure out how to get the critical points for this....

Answer 1

i remember how to get critical numbers for y=f(x). you find where f' is 0 and where f' DNE in the domain of f. would we do the same thing here? let me look it up

Answer 2

here is an example http://www.math.wvu.edu/~hjlai/Teaching/Tip-Pdf/Tip3-30.pdf

Answer 3

I have to make d/dx = 0 to find the critical but i can not figure out what it will be.

Answer 4

you might have to solve one of the equations for y or x and plug it into the other equation to find either x or y depending on what you solved for in the first one let me take a deeper look

Answer 5

the only solution i got is through quadratic but is that the only way?

Answer 6

This problem is ridiculous. I can't imagine taking derivatives and using the second partials test CANNOT be the way to do it. Have you done lagrange multipliers or polar coordinates?

Answer 7

I got this for homework and I am killing myself over it

Answer 8

how would i use lagranges for this?

Answer 9

Ha, you can't use Lagrange because there's only one function and no constraints. Was this problem all of your homework assignment? I am definitely thinking there are polar coordinates involved because of all the squares. I guess finding Fxx, Fxy, and Fyy would be the next step... nasty.