What is the extreme (20)/r+5pir^2 ?

The extreme (20)/r+5pir^2 is Minimum(\sqrt[3]{2/pi},10*2^{2/3}\sqrt[3]{pi}+5pi(2/pi)^{2/3})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme (20)/r+5pir^2

extreme

Minimum (3 \frac{2}{π}, 10 \cdot 2^{\frac{2}{3}} 3 π + 5 π (\frac{2}{π})^{\frac{2}{3}})

Solution steps

f^{'} (r) = - \frac{20}{r ^{2}} + 10 π r

Find intervals:

Decreasing

: - \infty < r < 0,

Decreasing

: 0 < r < \frac{3 4}{3 2 3 π},

Increasing

: \frac{3 4}{3 2 3 π} < r < \infty

Plug

r = 3 \frac{2}{π}

into

\frac{20}{r} + 5 π r^{2} : 10 \cdot 2^{\frac{2}{3}} 3 π + 5 π (\frac{2}{π})^{\frac{2}{3}}

Minimum (3 \frac{2}{π}, 10 \cdot 2^{\frac{2}{3}} 3 π + 5 π (\frac{2}{π})^{\frac{2}{3}})

What is the extreme (20)/r+5pir^2 ?
The extreme (20)/r+5pir^2 is Minimum(\sqrt[3]{2/pi},10*2^{2/3}\sqrt[3]{pi}+5pi(2/pi)^{2/3})