What is the extreme f(x,y)=sqrt(5-yln(x)) ?

The extreme f(x,y)=sqrt(5-yln(x)) is Saddle(1,0)

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extreme f(x,y)=sqrt(5-yln(x))

extreme points

f (x, y) = 5 - y ln (x)

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{ln ^{2} ( x )}{4 ( 5 - y ln ( x ) ) ^{\frac{3}{2}}}

D (x, y) = - \frac{y ln ^{2} ( x ) + 10}{8 x ^{2} ( - y ln ( x ) + 5 ) ^{2}}

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

f (x) = x^{2} + 4

f (x) = x^{2} - 7

f (x) = \frac{1}{3} x^{3} - x + 9

f (x) = - x^{3} - 15 x^{2}

f (x) = \frac{- x ^{2} - 6 x - 14}{x + 5}

What is the extreme f(x,y)=sqrt(5-yln(x)) ?
The extreme f(x,y)=sqrt(5-yln(x)) is Saddle(1,0)