What is the extreme 40000x+30000y-8x^2-15y^2-10xy ?

The extreme 40000x+30000y-8x^2-15y^2-10xy is Maximum(45000/19 , 4000/19)

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extreme 40000x+30000y-8x^2-15y^2-10xy

extreme points

40000 x + 30000 y - 8 x^{2} - 15 y^{2} - 10 x y

Maximum (\frac{45000}{19}, \frac{4000}{19})

Solution steps

Find the critical points:

(\frac{45000}{19}, \frac{4000}{19})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 30

D (x, y) = 380

Check the sign of at each critical point

Check critical point

(\frac{45000}{19}, \frac{4000}{19}) :

Maximum

Maximum (\frac{45000}{19}, \frac{4000}{19})

f (x) = \frac{- x ^{2}}{100} + x

f (x, y) = x^{2} y + y^{2} + 8 x

f (x) = x (15 - 48 + 2 x) (\frac{48}{2} - x)

7 sin (x) + 7 cos (x)

f (x) = 310 x^{2} - 1860 x^{3}

What is the extreme 40000x+30000y-8x^2-15y^2-10xy ?
The extreme 40000x+30000y-8x^2-15y^2-10xy is Maximum(45000/19 , 4000/19)