Identify and determine the nature of the critical points of

Solution

f(x,y) = 2xy - 2x^2 -5y^2 + 4y -3 fx = 2y - 4x fy = 2x - 10y + 4 for critical points, fx = 0, fy = 0 for fx = 0, 2y = 4x y = 2x for fy = 0 2x - 10y + 4 = 0 y-10y + 4 = 0 9y = 4 y = 4/9 x = 2/9 so the critical point is (2/9, 4/9) fxx = -4 fyy = -10 fxy = 2 D = fxx*fyy - (fxy)^2 D = 40 - 4 = 36.....hence (2/9, 4/9) is the point of minima