Examine each function for relative extrema and saddle points

Examine each function for relative extrema and saddle points. f(x,y) = x^2-3xy+y^2. Please show your work.

Solution

fx=2x-3y = 0

fy=-3x+2y = 0

critical point (0,0)

fxx= 2

fyy=2

fxy=-3

test ------> If f_xxf_yy-f_xy² is NEGATIVE, then the point is neither a max nor a min, it is a SADDLE POINT.

2*2 - 9 = -5 so saddle at point (0,0)