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Popular >

extreme 9/2 x^2-ln(x)

Solution

extreme points

\frac{9}{2} x^{2} - ln (x)

Solution

Minimum (\frac{1}{3}, \frac{1}{2} + ln (3))

Solution steps

f^{'} (x) = 9 x - \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = \frac{1}{3}

into

\frac{9}{2} x^{2} - ln (x) : \frac{1}{2} + ln (3)

Minimum (\frac{1}{3}, \frac{1}{2} + ln (3))

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Frequently Asked Questions (FAQ)

What is the extreme 9/2 x^2-ln(x) ?
The extreme 9/2 x^2-ln(x) is Minimum(1/3 , 1/2+ln(3))