Functions Question 329
Question: If $ f(x),=\frac{x}{1+|x|} $ for $ x\in R, $ then $ f’(0)= $
[EAMCET 2003]
Options:
A) 0
B) 1
C) 2
D) 3
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ x<0\Rightarrow |x|=-x $
Þ $ f(x)=\frac{d}{dx}( \frac{x}{1-x} )=\frac{1}{{{(1-x)}^{2}}} $
Þ $ {{[{f}’(x)]}{x=0}}=1 $ . Again $ x>0 $
Þ $ |x|,=,x $ $ f(x)=\frac{d}{dx}( \frac{x}{1+x} )=\frac{1}{{{(1+x)}^{2}}}\Rightarrow {{[{f}’(x)]}{x=0}}=1 $
Þ $ {f}’(0)=1 $ .
BETA
