What is the extreme f(x,y)=-9y^2-5x^2+10y+4x ?

The extreme f(x,y)=-9y^2-5x^2+10y+4x is Maximum(2/5 , 5/9)

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extreme f(x,y)=-9y^2-5x^2+10y+4x

extreme points

f (x, y) = - 9 y^{2} - 5 x^{2} + 10 y + 4 x

Maximum (\frac{2}{5}, \frac{5}{9})

Solution steps

Find the critical points:

(\frac{2}{5}, \frac{5}{9})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 18

D (x, y) = 180

Check the sign of at each critical point

Check critical point

(\frac{2}{5}, \frac{5}{9}) :

Maximum

Maximum (\frac{2}{5}, \frac{5}{9})

x^{4} - 4 x^{3} + 7

x^{4} - 4 x^{3} + 4

f (x) = x^{\frac{1}{3} (4 x^{2} - 14 x - 224)}

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

y = 3 x^{2} - 2 x + 1

What is the extreme f(x,y)=-9y^2-5x^2+10y+4x ?
The extreme f(x,y)=-9y^2-5x^2+10y+4x is Maximum(2/5 , 5/9)