What is the extreme ln(x-y)+x^2+y ?

The extreme ln(x-y)+x^2+y is Saddle(-1/2 ,-3/2)

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extreme ln(x-y)+x^2+y

extreme points

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

Saddle (- \frac{1}{2}, - \frac{3}{2})

Solution steps

Find the critical points:

(- \frac{1}{2}, - \frac{3}{2})

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

D (x, y) = - \frac{2}{( x - y ) ^{2}}

Check the sign of at each critical point

Check critical point

(- \frac{1}{2}, - \frac{3}{2}) :

Saddle

Saddle (- \frac{1}{2}, - \frac{3}{2})

f (x) = x^{101} + x^{51} + x + 1

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

f (x, y) = 5 + 3 x^{2} + 3 y^{2} + 2 y^{3} + x^{3}

f (x, y) = 3 x^{2} + 5 x y - 7 y^{2} + 1

x + \frac{4}{x}

What is the extreme ln(x-y)+x^2+y ?
The extreme ln(x-y)+x^2+y is Saddle(-1/2 ,-3/2)