What is the extreme E(a,b)=(2a+b)^2-(a+b)(a-b) ?

The extreme E(a,b)=(2a+b)^2-(a+b)(a-b) is Minimum(0,0)

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extreme E(a,b)=(2a+b)^2-(a+b)(a-b)

extreme points

E (a, b) = (2 a + b)^{2} - (a + b) (a - b)

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial a ^{2}} = 4

D (a, b) = 8

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x, y) = x^{2} - y^{2} + 1

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

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

f (x) = \frac{1}{3} x^{3} + 5 x^{2} + 24 x + 7

f (x) = \frac{x ^{2} - 16 x + 64}{x - 10}

What is the extreme E(a,b)=(2a+b)^2-(a+b)(a-b) ?
The extreme E(a,b)=(2a+b)^2-(a+b)(a-b) is Minimum(0,0)