What is the extreme f(x,y)=5xln(1y-9)+5y-5 ?

The extreme f(x,y)=5xln(1y-9)+5y-5 is Saddle(-1,10)

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extreme f(x,y)=5xln(1y-9)+5y-5

extreme points

f (x, y) = 5 x ln (1 y - 9) + 5 y - 5

Saddle (- 1, 10)

Solution steps

Find the critical points:

(- 1, 10)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{5 x}{( y - 9 ) ^{2}}

D (x, y) = - \frac{25}{( y - 9 ) ^{2}}

Check the sign of at each critical point

Check critical point

(- 1, 10) :

Saddle

Saddle (- 1, 10)

f (x) = x^{3} - 12 x^{2} + 21 x - 8

f (x) = x^{3} - 12 x + 5, - 6 \leq x \leq 6

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

f (x) = 3 x + 3 sin (x)

\frac{6}{x ^{2} + 3}

What is the extreme f(x,y)=5xln(1y-9)+5y-5 ?
The extreme f(x,y)=5xln(1y-9)+5y-5 is Saddle(-1,10)