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: Plotting Derivatives

  1. Jan 19, 2010 #1
    The problem statement.

    Suppose x''(t) = 1 for [tex]1\leq(t)\leq2[/tex], and x''(t) = 0 for all other (t)

    (a) Plot x''(t) for [tex]0\leq(t)\leq3[/tex]
    (b) Plot x'(t) for [tex]0\leq(t)\leq3[/tex]. Assume x'(0) = 0
    (c) Plot x(t) for [tex]0\leq(t)\leq3[/tex]. Assume x(0) = 0

    The attempt at a solution

    I assumed 'x' being the vertical axis and 't' being the horizontal axis.

    For (a) I know that there are going to be two points at 1 and two points at 0.

    My main question is when I graph these plots should I treat points 0 and 3 on the t-axis as discontinuities, and just put a point of where they're at and not include them when connecting the non-zero points, or should I connect all the points together, despite the discontinuity?
  2. jcsd
  3. Jan 19, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi jayeffarr! :smile:

    (have a ≤ :wink:)
    Personally, I'd leave them disconnected …

    x''(t) has only one value for each t, so why pretend it has more? :wink:
  4. Jan 19, 2010 #3
    Would you say to do the same thing when it comes to plotting x' and x...

    Since x'(t) = t

    and the plot will be (0,0), (1,1), (2,2), (3,0).

    And x(t) = (1/2)t²

    and the plot will be (0,0), (1,0.5), (2,2), (3,0).

    ...and just draw a line between 1 & 2, while having solid circles and 1 & 3?

    Or are you saying just to plot the points without connecting ANY of them?
    Last edited: Jan 19, 2010
  5. Jan 20, 2010 #4


    User Avatar
    Science Advisor
    Homework Helper

    Not following you :redface:

    x'(t) is the area under the graph of x''(t).​
  6. Jan 20, 2010 #5


    User Avatar
    Science Advisor

    I don't know what you mean by "two points". The graph is the horizontal straight line at y= 1 between 1 and 2, the horizontal straight line at y= 0, the x-axis, for all other t.

    "at 3 on the t-xis"? x"(3)= 0 and is 0 for every point near t= 3. Did you mean t= 2? In any case, it really doesn't matter. Technically, the vertical line is not part of the graph but if you can notice that this forms a rectangle under the graph, that will help.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook