What is the extreme f(x)=-3x+ln(x),(0,3) ?

The extreme f(x)=-3x+ln(x),(0,3) is Maximum(1/3 ,-1-ln(3))

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extreme f(x)=-3x+ln(x),(0,3)

extreme

Maximum (\frac{1}{3}, - 1 - ln (3))

Solution steps

Find the critical points:

x = \frac{1}{3}

Domain of

- 3 x + ln (x), (0, 3) : 0 < x < 3

Find intervals:

Increasing

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

Decreasing

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

Plug the extreme point

x = \frac{1}{3}

into

- 3 x + ln (x) \Rightarrow y = - 1 - ln (3)

Maximum (\frac{1}{3}, - 1 - ln (3))

What is the extreme f(x)=-3x+ln(x),(0,3) ?
The extreme f(x)=-3x+ln(x),(0,3) is Maximum(1/3 ,-1-ln(3))