What is the extreme f(x)= 49/2 x^2-ln(x) ?

The extreme f(x)= 49/2 x^2-ln(x) is Minimum(1/7 , 1/2+ln(7))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)= 49/2 x^2-ln(x)

extreme

Minimum (\frac{1}{7}, \frac{1}{2} + ln (7))

Solution steps

f^{'} (x) = 49 x - \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{7},

Increasing

: \frac{1}{7} < x < \infty

Plug

x = \frac{1}{7}

into

\frac{49}{2} x^{2} - ln (x) : \frac{1}{2} + ln (7)

Minimum (\frac{1}{7}, \frac{1}{2} + ln (7))

What is the extreme f(x)= 49/2 x^2-ln(x) ?
The extreme f(x)= 49/2 x^2-ln(x) is Minimum(1/7 , 1/2+ln(7))