GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
126 views
The function f(x) = 1/(1+|x|) is____

(A) Differntiable and Continuous
(B) Not Differntiable and Not Continuous
(C) Continuous but not Differntiable

I know this is continuous everywhere because |X| will always be a positive value, how to check if it's differntiable or not?
asked in Calculus by Veteran (11.4k points)   | 126 views
continuous but not differentiable?

@vijay find left and right derivative...one will be -1 and other 1 means nt differentiable!!

@Sudsho
yes correct RHD=-1 and LHD=1 hence not differntiable

1 Answer

0 votes

Let us define the function as we have |x| here ..

So

f(x)    =    1 / (1 + x)   , if x >= 0

         =    1 / (1 - x)   , if x <= 0

For continuity , we check at x = 0 only , so 

LHL = RHL  = f(0)  =  1

f' (x)   =   - 1 / (1 + x)2  , if x >= 0

         =   -1 / (1 - x)2  * (-1)  ,  

         =    1 / (1 - x)2     , if x <= 0

So Left derivative  at x = 0  :  1

 Right derivative  at x = 0 :  -1

So as Left derivative !=  Right derivative here

Hence  f(x) is not differentiable at x  =  0

Hence the given function is continuous but not differentiable due to x = 0..

answered by Veteran (59.5k points)  
Check the function definition.
This is a 12th class question.. I can bet my solution to be correct @ManojK..

No problem whatsoever..

actually he meant ur conditions are a bit wrong...x>=0 x<=0...on x=0 fn is 1....thats it nthing else;

Here we can write like this also..No problem @sudsho..
Top Users Jan 2017
  1. Debashish Deka

    7090 Points

  2. Habibkhan

    4676 Points

  3. Vijay Thakur

    4224 Points

  4. saurabh rai

    4014 Points

  5. sudsho

    3982 Points

  6. Arjun

    3138 Points

  7. GateSet

    3088 Points

  8. santhoshdevulapally

    3004 Points

  9. Bikram

    2976 Points

  10. Sushant Gokhale

    2824 Points

Monthly Topper: Rs. 500 gift card

18,816 questions
23,786 answers
51,458 comments
20,133 users