Question

f(x,y)=x^2+kxy+y^2 for k's value is everyone, proof that (o,o) critical point

Answer 1

Well, why not just find\(f_x\) and \(f_y\), and compare values at \((0, 0)\)?

Answer 2

Since \[f_x=2x+ky\]\[f_y=2y+kx\]And both are equal to 0 at \((0, 0)\) so it should be a critical point everywhere.

Answer 3

*It should be a critical point for all k