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

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

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

critical points

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

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

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

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

f (x) = x^{2} - 6 x + 4

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

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

f (x) = x^{3} - 6 x^{2} + 9 x + 15

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