GATE CSE
First time here? Checkout the FAQ!
x
0 votes
99 views
The function y=|2-3x| is not differential at x=2/3, please prove it.
asked in Calculus by Veteran (14.4k points)   | 99 views
thanks pavan!
habib's method is also correct..since this fn is continuous for x=2/3, we can check directly by finding its derivative and then checking from left side and right side..both methods are fine!!

1 Answer

+3 votes
Best answer

We define the modulus function piecewise as :

F(x)   =   -(2 - 3x)   =   3x - 2   , for x < 2/3  and 

         =    2 - 3x    for x >= 2/3

So in order to check for differentiability , we check for left derivative and right derivative..

Here left derivative is w.r.t F(x)  =  3x - 2..

So d(F(x)) / dx = 0  ==> d/dx(3x - 2)   =   3 ..Hence left derivative is 3 at x = 3 [In fact at any point for x <= 2/3]

Now coming to right derivative , we have : F(x)  =   2 - 3x

So d(F(x)) / dx = 0  ==> d/dx(2 - 3x)   =   -3..Hence right derivative is -3 at x = 3 [In fact at any point x >= 2/3]

As at x = 2/3 , Left derivative != Right derivative , so we can conclude

F(x) is not differentiable at x = 2/3

answered by Veteran (65k points)  
edited by
we should find the left hand limit and right hand limit at that point to prove it is not differentiable
Top Users Feb 2017
  1. Arjun

    5490 Points

  2. Bikram

    4266 Points

  3. Habibkhan

    3972 Points

  4. Aboveallplayer

    3126 Points

  5. Debashish Deka

    2646 Points

  6. sriv_shubham

    2328 Points

  7. Smriti012

    2270 Points

  8. Arnabi

    2114 Points

  9. sh!va

    1780 Points

  10. mcjoshi

    1702 Points

Monthly Topper: Rs. 500 gift card

20,905 questions
26,051 answers
59,775 comments
22,189 users