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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Minimum (0, 0), Maximum (1, 2)

Solution steps

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

Find intervals:

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

3 x^{\frac{1}{2}} - x^{\frac{3}{2}} : 0

Minimum (0, 0)

Plug

x = 1

into

3 x^{\frac{1}{2}} - x^{\frac{3}{2}} : 2

Maximum (1, 2)

Minimum (0, 0), Maximum (1, 2)

f (x) = 3 x^{4} - 8 x^{3}

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

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

f (x, y) = 2 x^{2} + 3 x y + y^{2} + a x + 5

f (x) = 6 x

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