Hello, Jonathan!
Sorry, your set-up is all wrong . . .
We want the extreme values of with the constraint: .Find the extreme values of on the ellipse
Our function is: .
Then: .
Now solve that system . . .
Grrr... This problem has been stressing me out for the past half hour
Find the extreme values of f(x,y) = xy on the ellipse ((x^2)/8) + ((y^2)/2) = 1
i've gone ahead and figured out the gradient f and g and ended up with (we'll call L lambda since I don't know how to insert that
y = (Lx)/4
x = Ly
((x^2)/8) + ((y^2)/2) = 1
I've gotten it down to this system of equations but i'm having trouble solving for this. Any help is appreciate.
Wow... just wow... you made it so much easier.
I just figured it out using my same setup but this would of been so much easier. This is what I did
Eq. 1 = y = (Lx)/4
Eq. 2 = x = Ly
Eq. 3 = ((x^2)/8) + ((y^2)/2) = 1
I substituted Eq.2 into Eq.1 for the x value and ended up with L = +2 and -2
Taking the value of lambda of +2 I put it in Eq.2 and got x = 2y
I then subbed 2y for the x value in Eq.3 and ended up with a y value of +1 and -1. Finding x is simple and got +2 and -2
I ended with extreme values of 2 and -2 for my final answer. All in all though, your way seems WAYYY easier and i'm gonna try it right now. Thanks!