Applications Of Derivatives Question 114
Question: The function $ f(x)=\log (1+x)-\frac{2x}{2+x} $ is increasing on
[EAMCET 2002]
Options:
A) (0, $ \infty $ )
B) ( $ -\infty $ , 0)
C) $ (-\infty ,\infty ) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=\log (1+x)-\frac{2x}{2+x} $
$ \Rightarrow f’(x)=\frac{1}{1+x}-\frac{(2+x).(2-2x)}{{{(2+x)}^{2}}} $
therefore $ f’(x)=\frac{x^{2}}{(x+1){{(x+2)}^{2}}} $ Obviously, $ f’(x)>0 $ for all $ x>0 $
Hence $ f(x) $ is increasing on $ (0,\infty ) $ .
BETA
