Question

What are the critical points of these functions, if any?
f(x,y)=-x^2-8xy-y^2

Answer 1

a critical point is where all partial derivatives are 0

Answer 2

(x,y,f)=(0,0,0) is the only point.

\[{\delta f \over dx} = -2x-8y\ \ =0\]\[{\delta f \over dx} = -8x-2y\ \ =0\]

the solution is x=0,y=0