What is the extreme f(x)=xln(x^2-y) ?

The extreme f(x)=xln(x^2-y) is Saddle(0,-1)

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extreme f(x)=xln(x^2-y)

extreme points

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

Saddle (0, - 1)

Solution steps

Find the critical points:

(0, - 1)

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

D (x, y) = - \frac{3 x ^{2} - y}{( x ^{2} - y ) ^{3}}

Check the sign of at each critical point

Check critical point

(0, - 1) :

Saddle

Saddle (0, - 1)

y = 3 x^{5} - 20 x^{3}

F (x, y) = 5 x y^{3} - y^{4} + \frac{x ^{2}}{2}

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

f (x, y) = 2 x^{3} - y^{3} - 24 x + 27 y - 2

f (x) = (x + 2)^{3}

What is the extreme f(x)=xln(x^2-y) ?
The extreme f(x)=xln(x^2-y) is Saddle(0,-1)