Question

How do you optimize `f(x,y)=x^2-3y^2` subject to `x^3-y^2=8`?

Answer 1

There is no finite extreme value.

Explanation:

Using `y^2=x^3-8`,
f(x, y) = g(x) = `-3x^3+x^2+24`'
`d/dxg(x)=-9x^2+2x=0 to x =0 or 2/9`
`y^2 < 0`,
So, these points (x, y) are unreal.
For y to be real, `x>=2`..