What is the extreme f(x,y)=33x+66y+xy-x^2-3y^2 ?

The extreme f(x,y)=33x+66y+xy-x^2-3y^2 is Maximum(24,15)

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extreme f(x,y)=33x+66y+xy-x^2-3y^2

extreme points

f (x, y) = 33 x + 66 y + x y - x^{2} - 3 y^{2}

Maximum (24, 15)

Solution steps

Find the critical points:

(24, 15)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6

D (x, y) = 11

Check the sign of at each critical point

Check critical point

(24, 15) :

Maximum

Maximum (24, 15)

f (x) = 3 x + 4 32.5 - x^{2}

8 x^{2} - 8 x^{4}

f (x) = 6 x^{2} - 10 y^{2}

f (x) = x^{4} - 4 x - 6

f (x, y) = x^{3} + y^{3} - 12 x - 15 y

What is the extreme f(x,y)=33x+66y+xy-x^2-3y^2 ?
The extreme f(x,y)=33x+66y+xy-x^2-3y^2 is Maximum(24,15)