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Popular >

extreme f(x)=3x-ln(3x)

Solution

extreme points

f (x) = 3 x - ln (3 x)

Solution

Minimum (\frac{1}{3}, 1)

Solution steps

f^{'} (x) = 3 - \frac{1}{x}

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{1}{3}

into

3 x - ln (3 x) : 1

Minimum (\frac{1}{3}, 1)

Popular Examples

domain of (x^2-16)/(x^2-1)domain

\frac{x ^{2} - 16}{x ^{2} - 1}

domain of f(x)= x/(x^2+4)domain

f (x) = \frac{x}{x ^{2} + 4}

asymptotes of f(x)=(x^2-5x+10)/(x+5)asymptotes

f (x) = \frac{x ^{2} - 5 x + 10}{x + 5}

inverse of 10cos(6x)+2 inverse

10 cos (6 x) + 2

domain of f(x)=(2x-1)/(x-4)domain

f (x) = \frac{2 x - 1}{x - 4}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=3x-ln(3x) ?
The extreme f(x)=3x-ln(3x) is Minimum(1/3 ,1)