Try setting
That is,
And solve for and .
This should give you four points which can be classified using the Hessian matrix.
The function I have to find the relative extreme for is f(x,y)= x^3 + y^3 + 3x^2 - 3y^2 the question didn't say it was subject to any constraints and the only ones we,be doing have been subject to the constraint x^2+y^2=1 so I'm not sure what to do for this one, thanks in advance
Try setting
That is,
And solve for and .
This should give you four points which can be classified using the Hessian matrix.
The partial derivatives are correct. The four critical points are:
Classifying a critical point means to determine whether it's a minimum, maximum or a saddle point.
For this you can use the Hessian matrix
.
Take it's determinant:
Then any given critical point is
1. a local minimum if and in the point,
2. a local maximum if and in the point,
3. a saddle point if in the point.
If the test is inconclusive.
Using this I got:
and are saddle points.
is a local minimum, with
is a local maximum, with
I suggest you try it yourself and see if you get the same results.