What is the extreme f(x,y)=8xln(x)y ?

The extreme f(x,y)=8xln(x)y is Saddle(1,0)

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extreme f(x,y)=8xln(x)y

extreme points

f (x, y) = 8 x ln (x) y

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 64 (ln (x) + 1)^{2}

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

f (x) = \frac{1}{4} x^{4} - 2 x^{3} + 2

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

f (x) = x^{3} + 3 x^{2} + 9, 0 \leq x \leq 10

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

1.5 x^{2} + 45 x + 15000

What is the extreme f(x,y)=8xln(x)y ?
The extreme f(x,y)=8xln(x)y is Saddle(1,0)