What is the critical f(x,y)=x^2-y-ln(xy) ?

The critical f(x,y)=x^2-y-ln(xy) is (1/(sqrt(2)),-1),(-1/(sqrt(2)),-1)

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critical f(x,y)=x^2-y-ln(xy)

critical points

f (x, y) = x^{2} - y - ln (x y)

(\frac{1}{2}, - 1), (- \frac{1}{2}, - 1)

Solution steps

x^{2} - y - ln (x y)

Find where

\nabla f (x, y)

is equal to zero or undefined

(\frac{1}{2}, - 1), (- \frac{1}{2}, - 1)

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

3 x^{2} y + y^{3} - 3 x^{2} - 3 y^{2} + 2

\frac{4 x ^{2} + 1}{x ^{2} + x + 16}

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

f (x) = 1 - x^{4} - y^{4}

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