What is the extreme f(x,y)=e^{yln(x)} ?

The extreme f(x,y)=e^{yln(x)} is Saddle(1,0)

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extreme f(x,y)=e^{yln(x)}

extreme points

f (x, y) = e^{y l n (x)}

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

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

D (x, y) = y^{2} x^{2 y - 2} ln^{2} (x) - y x^{2 y - 2} ln^{2} (x) - x^{2 (y - 1)} - 2 y x^{2 y - 2} ln (x) - y^{2} x^{2 (y - 1)} ln^{2} (x)

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

f (x) = - 1 + 3 x + x^{2}

f (x) = 2 x - 3, 0 \leq x \leq 2

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

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

x (r, t) = 2 r (2 t)

What is the extreme f(x,y)=e^{yln(x)} ?
The extreme f(x,y)=e^{yln(x)} is Saddle(1,0)