Find the extremum of the function z = x ^ 2-xy + y ^ 2-3y, and point out the maximum and minimum Need calculus process

Find the extremum of the function z = x ^ 2-xy + y ^ 2-3y, and point out the maximum and minimum Need calculus process

Z'x = 2x-y = 0, y = 2xz'y = - x + 2y-3 = 0, substituting y to get: - x + 4x-3 = 0, x = 1, so y = 2A = Z "XX = 2B = Z" xy = - 1C = Z "YY = 2ac-b ^ 2 = 4-1 = 3 > 0, and a > 0, so it is a minimum. Z (1,2) = 1-1 * 2 + 2 ^ 2-3 * 2 = 1-2 + 4-9 = - 6, so the function has only one minimum, Z (1,2) = - 6

Find the extremum of binary function z = x ^ 2 + XY + y ^ 2x-y, and determine whether it is a maximum or a minimum········

Let a = Z be the second partial derivative of X, B = Z be the mixed partial derivative of X, y, C = Z be the second partial derivative of Y. take each stationary point into a, B, C respectively, then a > 0 and AC-B ^ 2 > 0. This point is the minimum point, A0, this point is the maximum point, AC-B ^ 2

Find the extremum of binary function f (x, y) = 4x ^ 2 + 3Y ^ 2-xy-20x-21y + 100

As a function of X, the formula is as follows:
f（x）=4*[x-（y+20）/8]^2-4[(y+20)/8]^2+3y^2-21y+100
=4*[x-（y+20）/8]^2+47/16*(y-4)^2+28
So when x = (y + 20) / 8, y = 4, that is, x = 3, y = 4, f gets Fmin = 28