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

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

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critical f(x)=y^2x-yx^2+xy

critical points

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

(\frac{1}{3}, - \frac{1}{3}), (0, - 1)

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(\frac{1}{3}, - \frac{1}{3}), (0, - 1)

f (x) = 2 x^{3} - 6 x^{2} - 18 x + 7

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

f (x, y) = \frac{1}{3} x^{3} + \frac{1}{3} y^{3} - x - y + 10

f (x) = 12 x^{2} - 96 x + 144

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

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