What is the extreme f(x)=x^5*ln(x) ?

The extreme f(x)=x^5*ln(x) is Minimum(1/(\sqrt[5]{e)},-1/(5e))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^5*ln(x)

extreme

Minimum (\frac{1}{5 e}, - \frac{1}{5 e})

Solution steps

f^{'} (x) = 5 x^{4} ln (x) + x^{4}

Find intervals:

Decreasing

: 0 < x < \frac{1}{5 e},

Increasing

: \frac{1}{5 e} < x < \infty

Plug

x = \frac{1}{5 e}

into

x^{5} \cdot ln (x) : - \frac{1}{5 e}

Minimum (\frac{1}{5 e}, - \frac{1}{5 e})

What is the extreme f(x)=x^5*ln(x) ?
The extreme f(x)=x^5*ln(x) is Minimum(1/(\sqrt[5]{e)},-1/(5e))