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

The critical f(x,y)=x^2y^2-2/3 x^3-2/3 y^3 is (0,0),(0,0),(1,1)

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critical f(x,y)=x^2y^2-2/3 x^3-2/3 y^3

critical points

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

(0, 0), (0, 0), (1, 1)

Solution steps

x^{2} y^{2} - \frac{2}{3} x^{3} - \frac{2}{3} y^{3}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (0, 0), (1, 1)

- x^{4} + 8 x^{2} + 2

x^{2} + y^{2} + x^{2} y + 4

f (x) = - 4 x^{3} + 9 x^{2} - 4 x

f (x) = x^{2} - 24 x + 6

f (x) = I n (x x^{2} - 1)

What is the critical f(x,y)=x^2y^2-2/3 x^3-2/3 y^3 ?
The critical f(x,y)=x^2y^2-2/3 x^3-2/3 y^3 is (0,0),(0,0),(1,1)