What is the extreme f(x,y)=-5x^2-6y^2+5x-12y+5 ?

The extreme f(x,y)=-5x^2-6y^2+5x-12y+5 is Maximum(1/2 ,-1)

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extreme f(x,y)=-5x^2-6y^2+5x-12y+5

extreme points

f (x, y) = - 5 x^{2} - 6 y^{2} + 5 x - 12 y + 5

Maximum (\frac{1}{2}, - 1)

Solution steps

Find the critical points:

(\frac{1}{2}, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 12

D (x, y) = 120

Check the sign of at each critical point

Check critical point

(\frac{1}{2}, - 1) :

Maximum

Maximum (\frac{1}{2}, - 1)

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

f (x, y) = 2 x^{2} + 2 y^{2} - 16 x + 16 y

x^{2} (2 + y^{2}) + y ln (y)

3 x 2 + 3 y 2 + 3 z 2 + 2 y - 2 z = 9

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

What is the extreme f(x,y)=-5x^2-6y^2+5x-12y+5 ?
The extreme f(x,y)=-5x^2-6y^2+5x-12y+5 is Maximum(1/2 ,-1)