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

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

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

critical points

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

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

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

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

f (x) = 45 x^{3} - 3 x^{5}

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

3 x^{2} - x - 2

2 x^{3} - 3 x^{2} - 12 x + 1

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

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