What is the extreme P(a,b)=a^2-6a+9-b^2 ?

The extreme P(a,b)=a^2-6a+9-b^2 is Saddle(3,0)

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extreme P(a,b)=a^2-6a+9-b^2

extreme points

P (a, b) = a^{2} - 6 a + 9 - b^{2}

Saddle (3, 0)

Solution steps

Find the critical points:

(3, 0)

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

D (a, b) = - 4

Check the sign of at each critical point

Check critical point

(3, 0) :

Saddle

Saddle (3, 0)

f (x, y) = x^{3} + y^{3} + 15 x y

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

f (x) = x ln (\frac{x}{3}), 0.1 \leq x \leq 3

f (x) = 2 x^{3} - 6 x^{2} + 6 x - 8

x^{3} - 27 x + 51

What is the extreme P(a,b)=a^2-6a+9-b^2 ?
The extreme P(a,b)=a^2-6a+9-b^2 is Saddle(3,0)