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Homework Help: Function of a given derivative (calc I)

  1. Sep 20, 2008 #1
    I was given a graph of a derivative, f'(x), and I have determined that it's formula is:
    [tex]f'(x)=-abs(x-1)+1[/tex]
    It wants to know what the function f(x) is, as in the formula given that f(1)=0. I would be able to do this except I can't figure out what the function would BASICALLY look like! what would the function f(x) look like if its derivative is f'(x)=abs(x)? I know that the value of the derivative increases until x=1, where it then decreases, so it has somewhat of a mound shape, and the point (1,1) exists on the function of the derivative, so would it be a peak? i know it cant be an asymptote, but is a peak some kind of exception where the derivative ressembles the function itself?

    I just need a push in the right direction of what the original function may look like.:confused:
     
  2. jcsd
  3. Sep 20, 2008 #2

    statdad

    User Avatar
    Homework Helper

    Note that

    [tex]
    |x| = \begin{cases}
    \hphantom{-}x, & \text{ if } x \ge 0\\
    -x, & \text{ if } x < 0
    \end{cases}
    [/tex]
     
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