What is the extreme f(x)=7x^2+3/x ?

The extreme f(x)=7x^2+3/x is Minimum(\sqrt[3]{3/14},7(3/14)^{2/3}+3^{2/3}\sqrt[3]{14})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=7x^2+3/x

extreme

Minimum (3 \frac{3}{14}, 7 (\frac{3}{14})^{\frac{2}{3}} + 3^{\frac{2}{3}} 314)

Solution steps

f^{'} (x) = 14 x - \frac{3}{x ^{2}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3 \frac{3}{14},

Increasing

: 3 \frac{3}{14} < x < \infty

Plug

x = 3 \frac{3}{14}

into

7 x^{2} + \frac{3}{x} : 7 (\frac{3}{14})^{\frac{2}{3}} + 3^{\frac{2}{3}} 314

Minimum (3 \frac{3}{14}, 7 (\frac{3}{14})^{\frac{2}{3}} + 3^{\frac{2}{3}} 314)

What is the extreme f(x)=7x^2+3/x ?
The extreme f(x)=7x^2+3/x is Minimum(\sqrt[3]{3/14},7(3/14)^{2/3}+3^{2/3}\sqrt[3]{14})