What is the extreme f(x)=15x+18y-2x^2+2xy+3y^2 ?

The extreme f(x)=15x+18y-2x^2+2xy+3y^2 is Saddle(27/14 ,-51/14)

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extreme f(x)=15x+18y-2x^2+2xy+3y^2

extreme points

f (x) = 15 x + 18 y - 2 x^{2} + 2 x y + 3 y^{2}

Saddle (\frac{27}{14}, - \frac{51}{14})

Solution steps

Find the critical points:

(\frac{27}{14}, - \frac{51}{14})

\frac{\partial ^{2} f}{\partial x ^{2}} = 6

D (x, y) = - 28

Check the sign of at each critical point

Check critical point

(\frac{27}{14}, - \frac{51}{14}) :

Saddle

Saddle (\frac{27}{14}, - \frac{51}{14})

f (x, y) = x^{3} - 12 x + y^{2} + 6 y + 14

f (x) = x^{- 7} ln (x)

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

y = \frac{5 x ^{2}}{( x - 4 ) ^{2}}

f (x) = x (x - 10)^{2}

What is the extreme f(x)=15x+18y-2x^2+2xy+3y^2 ?
The extreme f(x)=15x+18y-2x^2+2xy+3y^2 is Saddle(27/14 ,-51/14)