What is the extreme Q(a,b)=7a(a-2b)+a(a-3b)+2a^2-8b^2 ?

The extreme Q(a,b)=7a(a-2b)+a(a-3b)+2a^2-8b^2 is Saddle(0,0)

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extreme Q(a,b)=7a(a-2b)+a(a-3b)+2a^2-8b^2

extreme points

Q (a, b) = 7 a (a - 2 b) + a (a - 3 b) + 2 a^{2} - 8 b^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial a ^{2}} = - 16

D (a, b) = - 609

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

g (y, z) = y^{2} z^{3} + π yz

f (x) = y^{2} + x y + 3 y + 2 x + 3

f (x) = \frac{x}{1 + x}

f (x) = 4 x^{2} - 1

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

What is the extreme Q(a,b)=7a(a-2b)+a(a-3b)+2a^2-8b^2 ?
The extreme Q(a,b)=7a(a-2b)+a(a-3b)+2a^2-8b^2 is Saddle(0,0)