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Extreme value of multivariate function in higher mathematics
Partial derivative of f(x, y) to x =4 -2x=0, x=2.

Partial derivative of f(x, y) to y =-4-2y=0, y=-2.

The second derivative of f(x, y) to x =-2

The second derivative of f(x, y) to y =-2

The partial derivative of f(x, y) to x and then to y =0.

Because -2 *-2-0 2 = 4 > 0, (2, -2) is an extreme value.

F(x, y) to x Second order =-2

f(2,-2)=8