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

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

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

critical points

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

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

Solution steps

x^{2} + y^{2} + \frac{1}{x ^{2} y ^{2}}

Find where

\nabla f (x, y)

is equal to zero or undefined

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

f (x) = x^{\frac{2}{3}} (x - 1)

f (x) = \frac{1}{7} x^{7} - a^{6} x

(x - 1)^{2} (x + 2)

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

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

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