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

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

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extreme f(x)=e^xln(x)y

extreme

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

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

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)