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

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

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critical f(x,y)=2xy-1/2 (x^4+y^4)+1

critical points

f (x, y) = 2 x y - \frac{1}{2} (x^{4} + y^{4}) + 1

(0, 0), (- 1, - 1), (1, 1)

Solution steps

2 x y - \frac{1}{2} (x^{4} + y^{4}) + 1

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- 1, - 1), (1, 1)

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

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

f (x) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y

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

\frac{4 x ^{2} + 2}{3 x - 1}

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