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

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

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

critical points

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

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

Solution steps

x y - x^{4} - y^{4}

Find where

\nabla f (x, y)

is equal to zero or undefined

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

80 x^{3} - 3 x^{5}

2 x - x^{2} - x y

2 x^{3} + x^{2} + 2 x

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

f (x) = e^{4 x} (48 x^{2} + 3)

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