I need to find the critical points for the function
$f(x) = 3(x^2 + y^2) – 2(x^3 – y^3) + 6xy$ and also test whether they are maxima/minima/saddle point.
Now the only critical point is (0,0)
however at (0,0) $rt – s^2 =0$ then second derivative test fails,
If I take the line $y = -x$ then
$f(x, -x) = -4x^3$ then clearly for along the neighborhood of $(0,0)$ $f$ has both positive and negative values .
Hence , $(0,0)$ is a saddle point .
Is my solution and answer correct ? Can someone please verify ?
Thank you.
Best Answer
The question has already been answered in the comments, I am just answering for the sake of completeness so that it does not remain unsolved.
The process is correct and $(0,0)$ is the saddle point for the given function.