What is the extreme f(x,y)=-7y^2-3x^2+15y+9x ?

The extreme f(x,y)=-7y^2-3x^2+15y+9x is Maximum(3/2 , 15/14)

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extreme f(x,y)=-7y^2-3x^2+15y+9x

extreme points

f (x, y) = - 7 y^{2} - 3 x^{2} + 15 y + 9 x

Maximum (\frac{3}{2}, \frac{15}{14})

Solution steps

Find the critical points:

(\frac{3}{2}, \frac{15}{14})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 14

D (x, y) = 84

Check the sign of at each critical point

Check critical point

(\frac{3}{2}, \frac{15}{14}) :

Maximum

Maximum (\frac{3}{2}, \frac{15}{14})

f (x, y) = \frac{x y + x - y + 2}{x ^{2} y + 1}

f (x, y) = x^{10} - y^{10} - 10 x + 10 y - 1

y = x^{3} - 3 x^{2} + 4

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

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

What is the extreme f(x,y)=-7y^2-3x^2+15y+9x ?
The extreme f(x,y)=-7y^2-3x^2+15y+9x is Maximum(3/2 , 15/14)