What is the extreme 5xy+4ln(x)+10y ?

The extreme 5xy+4ln(x)+10y is Saddle(-2, 2/5)

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extreme 5xy+4ln(x)+10y

extreme points

5 x y + 4 ln (x) + 10 y

Saddle (- 2, \frac{2}{5})

Solution steps

Find the critical points:

(- 2, \frac{2}{5})

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

D (x, y) = - 25

Check the sign of at each critical point

Check critical point

(- 2, \frac{2}{5}) :

Saddle

Saddle (- 2, \frac{2}{5})

f (x, y) = x^{2} + y^{2} + 2 x - 4 y + 2

f (x) = 3 x^{4} + 8 x^{3} - 14 x^{2} - 24 x + 17

f (x, y) = \frac{x + y}{x + y}

f (x, y) = x^{2} - y^{2} + 4 x + 2 y

f (x) = 5 x^{2} - 3 x + 1, - 3 \leq x \leq 3

What is the extreme 5xy+4ln(x)+10y ?
The extreme 5xy+4ln(x)+10y is Saddle(-2, 2/5)