I have to find and classify the stationary points of
So:
Have I done this right? How would I classify this?
Hello, billym!
I will assume that are positive.
Find and classify the stationary points of:
. .
There are four stationary points to examine: .
We have: .
Then: .
At . . . saddle point at
At . . . saddle point at
At . . . extreme point
. . At . . . minimum at
At . . . extreme point
. . At . . . maximum at
Yes, it looks fiine (just check the cases in red above), and now (a,b) is a saddle point (also called sometimes stationary point) iff , so that the function's Hessian (the matrix whose determinant you denoted by ) is indefinite (if you don't know these terms from linear algebra, which would be odd since you're studying multiariable calculus then just forget them...for now).
Tonio