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Thread: How to plot this graph with given table? Am I doing this right?

  1. #1
    Member nautica17's Avatar
    Aug 2009

    How to plot this graph with given table? Am I doing this right?

    I am working with increasing/decreasing functions and their concavity. I am given a table and I must make a graph based on what I am given. So I made my attempt, but I don't think this is right. Can someone help me out with this? I have no function to check my work. :|

    Sorry if the picture is large.. I don't know how to resize it on here.

    Edit: I'm also given the following:
    x-int: 0 and 4
    y-int: 0
    P(3) = 4

    Last edited by CaptainBlack; Mar 12th 2010 at 02:28 AM.
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  2. #2
    MHF Contributor
    Mar 2010
    Ok. You have a pretty difficult problem.

    Your x-intercepts are 0 and 4. From 0 to 3, P is decreasing and reaches a minimum at 3, but P(3)=4, so the graph must be discontinuous as you have shown. But also, from 3 to 4, P is increasing from its minimum of 4, but is zero at x=4. Again, the graph must be discontinuous.

    I've seen a lot of problems like this, and they're almost always continuous. If P(3) were -4 instead of 4, it would be continuous. Did you copy the problem wrong?

    Anyway, I'm sure you know that:
    P' positive means increasing, P' negative means decreasing
    P'' positive means concave up, P'' negative means concave down
    P' zero, P'' negative means a local maximum
    P' zero, P'' positive means a local minimum
    P' and P'' both zero means an inflection point

    below 0: decreasing, concave up - yes
    0: inflection point, P(0)=0 - yes
    0 to 1.5: decreasing, concave down - yes
    1.5: decreasing, neither concave up nor concave down - yes
    1.5 to 3: decreasing, concave up - yes
    3: minimum, P(3)=4 - not a minimum
    3 to 4, increasing, concave up - no (need to have second discontinuity)
    above 4: increasing, concave up, P(4)=0 - yes

    So you should have a graph with 3 pieces. If you do actually have P(3)=-4 instead of 4, you can move the middle piece into place. Let us know if you copied the problem wrong. If not, I would ask your professor/teacher/TA - let us know what happens. Even if you don't ask, let us know what the solution set says.
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