What is the extreme x^2+(400)/x ?

The extreme x^2+(400)/x is Minimum(2\sqrt[3]{25},4*25^{2/3}+(200)/(\sqrt[3]{25)})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme x^2+(400)/x

extreme

Minimum (2325, 4 \cdot 2 5^{\frac{2}{3}} + \frac{200}{3 25})

Solution steps

f^{'} (x) = 2 x - \frac{400}{x ^{2}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2325,

Increasing

: 2325 < x < \infty

Plug

x = 2325

into

x^{2} + \frac{400}{x} : 4 \cdot 2 5^{\frac{2}{3}} + \frac{200}{3 25}

Minimum (2325, 4 \cdot 2 5^{\frac{2}{3}} + \frac{200}{3 25})

What is the extreme x^2+(400)/x ?
The extreme x^2+(400)/x is Minimum(2\sqrt[3]{25},4*25^{2/3}+(200)/(\sqrt[3]{25)})