What is the extreme f(x)=x^2+2y^2-9x-12y ?

The extreme f(x)=x^2+2y^2-9x-12y is Minimum(9/2 ,3)

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extreme f(x)=x^2+2y^2-9x-12y

extreme points

f (x) = x^{2} + 2 y^{2} - 9 x - 12 y

Minimum (\frac{9}{2}, 3)

Solution steps

Find the critical points:

(\frac{9}{2}, 3)

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

D (x, y) = 8

Check the sign of at each critical point

Check critical point

(\frac{9}{2}, 3) :

Minimum

Minimum (\frac{9}{2}, 3)

f (x) = sin (\frac{x}{2})

f (x, y) = x^{3} + y^{3} - 3 x - 3 y + 20

f (x, y) = x^{3} + y^{2} - 4 x y + 17 x - 10 y + 8

f (x) = 2 x^{3} + 45 x^{2} + 84 x + 29

x^{3} - 12 x^{2} + 36 x

What is the extreme f(x)=x^2+2y^2-9x-12y ?
The extreme f(x)=x^2+2y^2-9x-12y is Minimum(9/2 ,3)