What is the critical f(x,y)=x^4+y^4+2x^2y^2+8a^2x^2-8a^2y^2 ?

The critical f(x,y)=x^4+y^4+2x^2y^2+8a^2x^2-8a^2y^2 is (0,0),(0,-2a),(0,2a),(0,0),(0,0)

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critical f(x,y)=x^4+y^4+2x^2y^2+8a^2x^2-8a^2y^2

critical points

f (x, y) = x^{4} + y^{4} + 2 x^{2} y^{2} + 8 a^{2} x^{2} - 8 a^{2} y^{2}

(0, 0), (0, - 2 a), (0, 2 a), (0, 0), (0, 0)

Solution steps

x^{4} + y^{4} + 2 x^{2} y^{2} + 8 a^{2} x^{2} - 8 a^{2} y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (0, - 2 a), (0, 2 a), (0, 0), (0, 0)

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

\frac{3 x}{x ^{3} + 5 x - 6}

f (x) = \frac{x ^{3}}{3} + \frac{7 x ^{2}}{2} + 6 x + 3

x^{3} - 6 x^{2} + 5

f (x) = 9 x (x + 8)^{\frac{1}{3}}

What is the critical f(x,y)=x^4+y^4+2x^2y^2+8a^2x^2-8a^2y^2 ?
The critical f(x,y)=x^4+y^4+2x^2y^2+8a^2x^2-8a^2y^2 is (0,0),(0,-2a),(0,2a),(0,0),(0,0)