1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Finding the particular anti derivative when given f'(x) and TWO f(value)s

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data

    Here is the question directly from the book:

    f'(x)=x^(-1/3), f(1)=1, f(-1)=-1, find f(x).

    2. Relevant equations



    3. The attempt at a solution

    So there are about ten of these types, and I am very confused. I am confused because if you solve for f(x) with f(a) you get a different value for c than if you solved for f(b).

    So finding f(x) I get f(x)=(3/2)x^(2/3) + c
    If I make f(x)=1 and x=1, I get the value of c to be -1/2
    But if I make f(x)=-1 and x=-1, I get the value of c to be -5/2..

    Thank you so much for your help in advance!
     
  2. jcsd
  3. Nov 26, 2011 #2
    Notice that f(0) is not defined. So you actually have two branches. So your function can be described as

    [tex]f(x)=\left\{\begin{array}{c}(3/2)x^{2/3} + c_1 ~\text{if}~x>0\\ (3/2)x^{2/3} + c_2 ~\text{if}~x<0 \end{array}\right.[/tex]
     
  4. Nov 26, 2011 #3
    So whenever f'(0)=DNE, the function f(x) can be written as a piecewise function?
     
  5. Nov 26, 2011 #4
    Indeed!!

    Do notice that you proved that the anti-derivative of a function is unique up to a constant. But you only proved that for functions that exists everywhere on an interval. If a function does not exist in a point, then the result isn't true anymore!!
     
  6. Nov 27, 2011 #5
    OK, thanks again! You helped tremendously.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...