What is the extreme f(x,y)=xln(y-x) ?

The extreme f(x,y)=xln(y-x) is Saddle(0,1)

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extreme f(x,y)=xln(y-x)

extreme points

f (x, y) = x ln (y - x)

Saddle (0, 1)

Solution steps

Find the critical points:

(0, 1)

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

D (x, y) = \frac{- x ( - 2 y + x ) - y ^{2}}{( - x + y ) ^{4}}

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Saddle (0, 1)

- 4.9 x^{2} + 24 x + 8

f (x, y) = x^{3} + 3 x y^{2} - 3 x^{2} - 3 y^{2} + 10

f (x) = - \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 1

f (x, y) = x^{3} + y^{3} - 3 x - 12 y + 13 e

f (x) = - \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 9

What is the extreme f(x,y)=xln(y-x) ?
The extreme f(x,y)=xln(y-x) is Saddle(0,1)