1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fundamental Theorem of Calculus properties

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a function f : [-1,1] ---> R such that f satisfies the following properties:

    a) f is continuous
    b) f is restricted to (-1,1) is differentiable
    c) its derivative f' is not differentiable on (-1,1)

    2. Relevant equations


    3. The attempt at a solution
    I kinda think that the mean value theorem and Theorem 2 of the fundamentals [tex]\int[/tex]f(x)dx = F(b)-F(a) got some link but I can't seem to get it. I do understand that for f'' not to exist, x should be undefined on the (-1,1). Please help.
     
  2. jcsd
  3. Apr 2, 2009 #2
    A read somewhere that a hint would be to begin with an absolute value and use [tex]\int[/tex]f(x)dx = F(b)-F(a) (fundamental theorem of calc prep 2) repeatedly.. but still puzzled
     
  4. Apr 2, 2009 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Start with c). Pick a nondifferentiable function on (-1,1) and integrate it to get f.
     
  5. Apr 3, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    |x| is a very simple function that is not differentiable at x= 0.
     
  6. Apr 3, 2009 #5
    You are right, but the OP is looking for a function such that it is once differentiable on (-1,1) but not twice, and is continuous of course on the same interval.

    Edit: ignore it!
     
  7. Apr 3, 2009 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, and combining |x| with Dick's suggestion gives exactly that!

    (Edit: Too late! I gotcha!)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fundamental Theorem of Calculus properties
Loading...