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})

f (x, y) = e^{\frac{( x ^{8} + y ^{8} )}{8}}

\frac{x ^{3} - 4 x}{x ^{3} - x}

f (x) = 14 cos (θ) + 7 sin^{2} (θ)

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

f (x) = 3 x^{2} - 96 x

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)