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: Derivative of a function

  1. Mar 5, 2014 #1
    Problem statement

    ImageUploadedByPhysics Forums1394018429.382539.jpg
    My question is for number 27.
    Revelant equation

    Attempt at a solution

    I'm not sure where to start.
    ImageUploadedByPhysics Forums1394018545.381550.jpg ImageUploadedByPhysics Forums1394018553.886597.jpg

    This is my teachers answer. I understand how the slope is 1 for x greater than -1 and that it is -2 at x greater than -1 and that there is a point at (0,-1) but I don't understand how they connect to form that final pic. I think I'm missing something ,can someone help me?
  2. jcsd
  3. Mar 5, 2014 #2
    Never mind I think I understand it now. I think I was just confused by the previous picture leading up to the answer.
  4. Mar 5, 2014 #3

    Maybe someone could elaborate on this for me? Thanks
  5. Mar 5, 2014 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    What does it mean for a function to be continuous ?
  6. Mar 6, 2014 #5
    That there are no breaks or holes
  7. Mar 6, 2014 #6


    User Avatar
    Science Advisor

    If f'(x)= 1, for x< -1, then f(x)= x+ C1 for some constant C1, for x< -1, so the graph is a straight line with slope 1.

    If f'(x)= -2, for x> -1, then f(x)= -2x+ C2 for some constant C2, for x> -1, so the graph is a straight line with slope -2.

    Since f is continuous, the two lines must meet at x= -1. That means that -1+ C1= -2(-1)+ C2.

    That, together with f(0)= C2= -1 is sufficient to determine both C2 and C1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted