What is the extreme f(x)=x^{1/5}(x+24) ?

The extreme f(x)=x^{1/5}(x+24) is Minimum(-4,-20*4^{1/5})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^{1/5}(x+24)

extreme

Minimum (- 4, - 20 \cdot 4^{\frac{1}{5}})

Solution steps

f^{'} (x) = \frac{6 ( x + 4 )}{5 x ^{\frac{4}{5}}}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

x^{\frac{1}{5}} (x + 24) : - 20 \cdot 4^{\frac{1}{5}}

Minimum (- 4, - 20 \cdot 4^{\frac{1}{5}})

What is the extreme f(x)=x^{1/5}(x+24) ?
The extreme f(x)=x^{1/5}(x+24) is Minimum(-4,-20*4^{1/5})