What is the critical f(x)=2(x-4)^2(y^2+3)+3y^2+12y ?

The critical f(x)=2(x-4)^2(y^2+3)+3y^2+12y is (4,-2)

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critical f(x)=2(x-4)^2(y^2+3)+3y^2+12y

critical points

f (x) = 2 (x - 4)^{2} (y^{2} + 3) + 3 y^{2} + 12 y

(4, - 2)

Solution steps

2 (x - 4)^{2} (y^{2} + 3) + 3 y^{2} + 12 y

Find where

\nabla f (x, y)

is equal to zero or undefined

(4, - 2)

x^{2} - 2

f (x) = x^{3} - 2 x y + y^{2} + 4

- 2 x^{2} - 12 x - 13

f (x, y) = x^{3} + y^{3} - 2 x y

f (x) = 8 x^{2} + 14 x y + 3 y^{2} + 10 x - 4

What is the critical f(x)=2(x-4)^2(y^2+3)+3y^2+12y ?
The critical f(x)=2(x-4)^2(y^2+3)+3y^2+12y is (4,-2)