What is the extreme P(x,y)=6x^2+19xy+15y^2-17y-11x+4 ?

The extreme P(x,y)=6x^2+19xy+15y^2-17y-11x+4 is Saddle(-7,5)

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extreme P(x,y)=6x^2+19xy+15y^2-17y-11x+4

extreme points

P (x, y) = 6 x^{2} + 19 x y + 15 y^{2} - 17 y - 11 x + 4

Saddle (- 7, 5)

Solution steps

Find the critical points:

(- 7, 5)

\frac{\partial ^{2} f}{\partial x ^{2}} = 30

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 7, 5) :

Saddle

Saddle (- 7, 5)

5 sin^{2} (x), 0 \leq x \leq π

f (x) = - x^{3} + 3 x - 11

f (x) = 2 x^{3} - 3 x^{2} - 4

f (x) = - 12 x^{3} + 2 x^{2} - 3

f (x) = x^{3} - 2 x^{2} - 15 x + 10 [- 2]

What is the extreme P(x,y)=6x^2+19xy+15y^2-17y-11x+4 ?
The extreme P(x,y)=6x^2+19xy+15y^2-17y-11x+4 is Saddle(-7,5)