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

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

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

critical points

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

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

f (x) = - \frac{x ^{3}}{3} + 25 x

\frac{3}{2} x^{2} + x^{3} + 3 y^{2}

f (x) = \frac{4 x ^{2}}{x ^{2} + 25}

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