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

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

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

critical points

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

(0, 0), (2, 1), (- 2, 1)

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (2, 1), (- 2, 1)

f (x) = \frac{1}{4} x^{4} - \frac{4}{3} x^{3} + \frac{3}{2} x^{2} + 1

f (x) = 2 x^{3} + 5 x^{2} - x + 1

f (x) = - 2 x + 5

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 7 x - 11 y

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

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