What is the extreme x^2+xy+3x+2y+5 ?

The extreme x^2+xy+3x+2y+5 is Saddle(-2,1)

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extreme x^2+xy+3x+2y+5

extreme points

x^{2} + x y + 3 x + 2 y + 5

Saddle (- 2, 1)

Solution steps

Find the critical points:

(- 2, 1)

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

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 2, 1) :

Saddle

Saddle (- 2, 1)

f (x) = x^{3} + 2 x^{2} - 5 x - 6

f (x) = \frac{1}{x ^{2} - 9}

y = 2 x^{3} - 3 x + 5

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

f (x) = \frac{1}{x ^{2} + y ^{2} + 1}