What is the extreme f(x,y)=14xy-x^3-7y^2 ?

The extreme f(x,y)=14xy-x^3-7y^2 is Saddle(0,0),Maximum(14/3 , 14/3)

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extreme f(x,y)=14xy-x^3-7y^2

extreme points

f (x, y) = 14 x y - x^{3} - 7 y^{2}

Saddle (0, 0), Maximum (\frac{14}{3}, \frac{14}{3})

Solution steps

Find the critical points:

(0, 0), (\frac{14}{3}, \frac{14}{3})

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

D (x, y) = 84 x - 196

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

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

Maximum

Saddle (0, 0), Maximum (\frac{14}{3}, \frac{14}{3})

f (x, y) = x^{2} + x y + y^{2} - 25 y + 208

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

y = \frac{x ( z + 2 )}{7}

x^{2} + 3

f (x) = 2 x 5 - 5 x

What is the extreme f(x,y)=14xy-x^3-7y^2 ?
The extreme f(x,y)=14xy-x^3-7y^2 is Saddle(0,0),Maximum(14/3 , 14/3)