What is the extreme f(x,y)=yln(5x+9y) ?

The extreme f(x,y)=yln(5x+9y) is Saddle(1/5 ,0)

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extreme f(x,y)=yln(5x+9y)

extreme points

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

Saddle (\frac{1}{5}, 0)

Solution steps

Find the critical points:

(\frac{1}{5}, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{9 ( 10 x + 9 y )}{( 5 x + 9 y ) ^{2}}

D (x, y) = \frac{- 225 y ( 10 x + 9 y ) - 625 x ^{2}}{( 5 x + 9 y ) ^{4}}

Check the sign of at each critical point

Check critical point

(\frac{1}{5}, 0) :

Saddle

Saddle (\frac{1}{5}, 0)

f (x) = ∣ - 3 x - 2 ∣, - 4 < x < 2

f (x) = 2 + 4 x + 100 x^{- 1}

f (x, y) = x^{2} + y^{2} - 12 x + 16 y

x^{\frac{1}{7}} + 1

f (x) = x^{3} + 6 x^{2} - 6 [- 8.3]

What is the extreme f(x,y)=yln(5x+9y) ?
The extreme f(x,y)=yln(5x+9y) is Saddle(1/5 ,0)