What is the critical f(x,y)=3y^2-2y^3-3x^2+6xy ?

The critical f(x,y)=3y^2-2y^3-3x^2+6xy is (0,0),(2,2)

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critical f(x,y)=3y^2-2y^3-3x^2+6xy

critical points

f (x, y) = 3 y^{2} - 2 y^{3} - 3 x^{2} + 6 x y

(0, 0), (2, 2)

Solution steps

3 y^{2} - 2 y^{3} - 3 x^{2} + 6 x y

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (2, 2)

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

x^{2} + 4

f (x, y) = x^{3} + y^{3} + 3 x^{2} - 3 y^{2} - 8

f (x) = x^{2} - 4 x + 1

f (x) = 3 x^{2} ln (x)

What is the critical f(x,y)=3y^2-2y^3-3x^2+6xy ?
The critical f(x,y)=3y^2-2y^3-3x^2+6xy is (0,0),(2,2)