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Popular >

extreme ln(-x)+ln(x+1)

Solution

extreme points

ln (- x) + ln (x + 1)

Solution

Maximum (- \frac{1}{2}, - 2 ln (2))

Solution steps

f^{'} (x) = - \frac{- 2 x - 1}{x ( x + 1 )}

Find intervals:

Increasing

: - 1 < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 0

Plug

x = - \frac{1}{2}

into

ln (- x) + ln (x + 1) : - 2 ln (2)

Maximum (- \frac{1}{2}, - 2 ln (2))

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Frequently Asked Questions (FAQ)

What is the extreme ln(-x)+ln(x+1) ?
The extreme ln(-x)+ln(x+1) is Maximum(-1/2 ,-2ln(2))