Question

Find the minimum and maximum values of the function subject to the given constraint
f(xy)=x^2+y^2 , x^4+y^4=8

Answer 1

Find f_x and f_y. Set them to zero. Solve for the critical points.
Then solve your equation x^4+y^4=8 for x OR y. Plug that in, solve for critical points. You could also set the two equal to see if there are in "corner" points. Then use the Hessian/discriminant to see if they are >0 or <0. If it is 0> then it is a saddle point. If it is >0 then you need to look at f_xx. If f_xx is POSITIVE, it is concave up and is a relative min. If f_xx is NEGATIVE, it is concave down and is a relative max. Then plug in the points into the original equation to get the height. Whichever is the highest/lowest is the ABSOLUTE max/min.

Answer 2

Let me know if you need more elaboration :P

Answer 3

okay, thank you I'm going to try now

Answer 4

Okay, just tell me if you get stuck.

Answer 5

I got through it no problem! thx :)

Answer 6

No problem :)