Find and classify the critical points of each function a fxy

Find and classify the critical points of each function
(a.) f(x,y) = x^2-xy+y^2+9x-6y+10

Answer: local min of -11 at (-4,1)

partial diff wrt x : 2x -y + 9 = 0 partial diff wrt y : -x + 2y - 6 = 0 solving : x = -4 , y=1 second derivative at x : 2 minimia second derivative wrt y : 2 , minima hence local minima at (-4,1)