Applications Of Derivatives Question 263
Question: If $ f(x)=\frac{1}{x+1}-\log ,(1+x),,x>0, $ then $ f $ is
[RPET 2002]
Options:
A) An increasing function
B) A decreasing function
C) Both increasing and decreasing function
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=\frac{1}{x+1}-\log (1+x) $
therefore $ {f}’(x)=-\frac{1}{{{(x+1)}^{2}}},-,\frac{1}{1+x} $
$ {f}’(x)=-[ \frac{1}{x+1}+\frac{1}{{{(x+1)}^{2}}} ] $
$ {f}’(x)=-ve $ , when $ x>0 $ or $ {f}’(x)<0 $ , $ \forall x>0 $ \ $ f(x) $ is decreasing function.
BETA
