What is the extreme f(x)=10xy-x^3-5y^2 ?

The extreme f(x)=10xy-x^3-5y^2 is Saddle(0,0),Maximum(10/3 , 10/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=10xy-x^3-5y^2

extreme points

f (x) = 10 x y - x^{3} - 5 y^{2}

Saddle (0, 0), Maximum (\frac{10}{3}, \frac{10}{3})

Solution steps

Find the critical points:

(0, 0), (\frac{10}{3}, \frac{10}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 10

D (x, y) = 60 x - 100

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(\frac{10}{3}, \frac{10}{3}) :

Maximum

Saddle (0, 0), Maximum (\frac{10}{3}, \frac{10}{3})

f (x) = \frac{x ^{3}}{3} - 5 x^{2} - 4

f (x) = x^{3} - 5 x + 2

f (x) = (x - 3) e^{x} + 3

x^{4} + x^{2}

f (x) = x^{7} - 4 x^{5} + 10

What is the extreme f(x)=10xy-x^3-5y^2 ?
The extreme f(x)=10xy-x^3-5y^2 is Saddle(0,0),Maximum(10/3 , 10/3)