What is the extreme f(x,y)=2xln(y^2-4) ?

The extreme f(x,y)=2xln(y^2-4) is Saddle(0,sqrt(5)),Saddle(0,-sqrt(5))

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extreme f(x,y)=2xln(y^2-4)

extreme

Saddle (0, 5), Saddle (0, - 5)

Solution steps

Find the critical points:

(0, 5), (0, - 5)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{4 x ( - y ^{2} - 4 )}{( y ^{2} - 4 ) ^{2}}

D (x, y) = - \frac{16 y ^{2}}{( y ^{2} - 4 ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 5) :

Saddle

Check critical point

(0, - 5) :

Saddle

Saddle (0, 5), Saddle (0, - 5)

What is the extreme f(x,y)=2xln(y^2-4) ?
The extreme f(x,y)=2xln(y^2-4) is Saddle(0,sqrt(5)),Saddle(0,-sqrt(5))