What is the extreme 5x^{2/3}-x^{5/3} ?

The extreme 5x^{2/3}-x^{5/3} is Minimum(0,0),Maximum(2,3*2^{2/3})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme 5x^{2/3}-x^{5/3}

extreme points

5 x^{\frac{2}{3}} - x^{\frac{5}{3}}

Minimum (0, 0), Maximum (2, 3 \cdot 2^{\frac{2}{3}})

Solution steps

f^{'} (x) = \frac{10 - 5 x}{3 x ^{\frac{1}{3}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

5 x^{\frac{2}{3}} - x^{\frac{5}{3}} : 0

Minimum (0, 0)

Plug

x = 2

into

5 x^{\frac{2}{3}} - x^{\frac{5}{3}} : 3 \cdot 2^{\frac{2}{3}}

Maximum (2, 3 \cdot 2^{\frac{2}{3}})

Minimum (0, 0), Maximum (2, 3 \cdot 2^{\frac{2}{3}})

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

f (x) = \frac{1}{1 - sin ( x )}

(4, 4), (- 2, - 4)

What is the extreme 5x^{2/3}-x^{5/3} ?
The extreme 5x^{2/3}-x^{5/3} is Minimum(0,0),Maximum(2,3*2^{2/3})