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

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

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

extreme points

f (x) = 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})

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210)

f (x) = - x^{3} + 3 x^{2} - 8

f (x) = 8 x^{2} - 2 x^{4}

P (q, s) = q + 2 + s

f (x) = \frac{5}{3} x^{3} - \frac{65}{2} x^{2} + 200 x - 1

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