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

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

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

critical points

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

(0, 0), (- \frac{1}{4}, - \frac{1}{4}), (\frac{1}{4}, \frac{1}{4})

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- \frac{1}{4}, - \frac{1}{4}), (\frac{1}{4}, \frac{1}{4})

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

f (x) = 12 x - 4 x^{3}

f (y) = x^{2} + 6 x + 9

2 x^{3} - 3 x^{2} - 12 x + 15

t^{\frac{3}{4}} - 6 t^{\frac{1}{4}}

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