Note that for real x and y, and , thus , and so , and thus is never zero.
--Kevin C.
I have this function and I am looking for the stationary points:
I started by trying to solve the two partial derivatives:
If , then becomes:
Thus , , or , so there are three stationary points at , , and , correct?
Next, if:
i.e.
then becomes... uh...
this is where I run into trouble.
Is ?
How do I go about finding other points? Are there other stationary points?
Hello, billym!
A small error in your derivatives, but your intentions were correct.
We have: .
From [1], we have: .
If , [2] becomes: .
. . So far, we have: .
From [2], we have: .
If , [1] becomes: .
If , [1] becomes: .
. . and we've already encountered these solutions.
Therefore, the stationary points are: .