I know that how to find relative maximum and minimum of function of two variables.
How can I determine function when $f(x,y,z)=x^2+y^2-z^2 $ has relative maximum or relative minimum?
Please give me hint. In general when does $f(x,y,z)$ have relative minimum or relative maximum? Thanks in advance.
Best Answer
I cut and paste from Wikipedia:
See the original page here.
What you learned for the 2D case is a particular trick to test the positivity of the hessian matrix evaluated at a critical point. In higher dimension you must write down the hessian matrix and compute its signature, unless the specific structure of your function allows some easier approach.