What is the extreme f(x,y)=xy+ln(x)+32y^2 ?

The extreme f(x,y)=xy+ln(x)+32y^2 is Saddle(-8, 1/8),Saddle(8,-1/8)

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extreme f(x,y)=xy+ln(x)+32y^2

extreme points

f (x, y) = x y + ln (x) + 32 y^{2}

Saddle (- 8, \frac{1}{8}), Saddle (8, - \frac{1}{8})

Solution steps

Find the critical points:

(- 8, \frac{1}{8}), (8, - \frac{1}{8})

\frac{\partial ^{2} f}{\partial x ^{2}} = 64

D (x, y) = - \frac{64}{x ^{2}} - 1

Check the sign of at each critical point

Check critical point

(- 8, \frac{1}{8}) :

Saddle

Check critical point

(8, - \frac{1}{8}) :

Saddle

Saddle (- 8, \frac{1}{8}), Saddle (8, - \frac{1}{8})

What is the extreme f(x,y)=xy+ln(x)+32y^2 ?
The extreme f(x,y)=xy+ln(x)+32y^2 is Saddle(-8, 1/8),Saddle(8,-1/8)