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

The critical f(x,y)=x^2y-2xy^2+3xy+4 is (-1, 1/2),(0, 3/2)

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

critical points

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

(- 1, \frac{1}{2}), (0, \frac{3}{2})

Solution steps

x^{2} y - 2 x y^{2} + 3 x y + 4

Find where

\nabla f (x, y)

is equal to zero or undefined

(- 1, \frac{1}{2}), (0, \frac{3}{2})

f (x) = \frac{- 9}{( x ^{2} - 9 ) x ^{2} - 9}

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

f (x) = 4 (x - 4)^{\frac{2}{3}}

\frac{- 2 x}{( 1 + x ^{2} ) ^{2}}

f (x) = 2 x^{3} - 21 x^{2} + 5

What is the critical f(x,y)=x^2y-2xy^2+3xy+4 ?
The critical f(x,y)=x^2y-2xy^2+3xy+4 is (-1, 1/2),(0, 3/2)