What is the extreme f(x)=x(x+3)^{1/2} ?

The extreme f(x)=x(x+3)^{1/2} is Maximum(-3,0),Minimum(-2,-2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x(x+3)^{1/2}

extreme points

f (x) = x (x + 3)^{\frac{1}{2}}

Maximum (- 3, 0), Minimum (- 2, - 2)

Solution steps

f^{'} (x) = \frac{3 x + 6}{2 ( x + 3 ) ^{\frac{1}{2}}}

Find intervals:

Decreasing

: - 3 < x < - 2,

Increasing

: - 2 < x < \infty

Plug

x = - 3

into

x (x + 3)^{\frac{1}{2}} : 0

Maximum (- 3, 0)

Plug

x = - 2

into

x (x + 3)^{\frac{1}{2}} : - 2

Minimum (- 2, - 2)

Maximum (- 3, 0), Minimum (- 2, - 2)

f (x, y) = 2 x + 4 y - x^{2} - y^{2} - 3

f (x) = 4 x^{3} - 36 x^{2} + 80 x

2 x - 4

f (x) = 4 x^{3} - 36 x^{2} + 81 x

y = (x - 1)^{3} + 3

What is the extreme f(x)=x(x+3)^{1/2} ?
The extreme f(x)=x(x+3)^{1/2} is Maximum(-3,0),Minimum(-2,-2)