What is the extreme f(x,y)=40000x+30000y-8x^2-15y^2-10xy ?

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

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extreme f(x,y)=40000x+30000y-8x^2-15y^2-10xy

extreme points

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

f (x) = x + \frac{30}{x}

\frac{5 x + 4}{x + x}

F (x, y) = x \cdot y + \frac{π \cdot ( \frac{x}{2} ) ^{2}}{2}

f (x) = - \frac{5 x ^{4}}{4} - \frac{4 x ^{3}}{3} - 4

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