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

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

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

extreme points

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

Maximum (1, 2)

Solution steps

Find the critical points:

(1, 2)

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

D (x, y) = 36

Check the sign of at each critical point

Check critical point

(1, 2) :

Maximum

Maximum (1, 2)

f (x) 2 x^{2} - 4 x - 1

5 cos^{2} (x), 0 \leq x \leq π

y = x^{3} - 6 x^{2} + 15

f (x) = (\frac{x ^{2} - 1}{( 5 - x ^{2} ) ^{0.5}})

f (x) = 2 x^{3} + 9 x^{2} - 60 x + 1

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