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Question

If f(x)=1(x+1)-log(1+x),x>0then f is


A

An increasing function

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B

A decreasing function

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C

Both increasing and decreasing function

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D

None of the above

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Solution

The correct option is B

A decreasing function


Step 1: Given information

f(x)=1(x+1)-log(1+x)

Step 2: Differentiation of given equation

f'(x)=-1(x+1)2-11+xf'(x)=-1(x+1)2+11+xf'(x)<0

when x>0orf'(x)<0,forallx>0

therefore, f(x)is decreasing function

Hence, the correct option is an option (B) A decreasing function.


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