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Partition Numbers

  1. Feb 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Use a graphing utility to approximate the partition numbers of the function f(x) to two decimal places. Then solve the following inequalities.
    (a) f(x)>0
    (b) f(x)<0
    Express all answers in interval notation
    2. Relevant equations



    3. The attempt at a solution
    The partition can be calculated by just finding the max and the min of the graph with my TI-83 Plus, right? It's solving the inequalities I'm having trouble with. What exactly is it asking for?
     
  2. jcsd
  3. Feb 21, 2008 #2

    Dick

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    What are the 'partition numbers' of a function f(x)?? Can you define that??
     
  4. Feb 21, 2008 #3
    wow..sorry

    brain fart. I'm a little flooded in work and lacking sleep..sorry.

    the function is f(x)=x^3-3x^2-2x+5
     
  5. Feb 21, 2008 #4

    Dick

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    I didn't mean define the function, I meant define the term 'partition numbers' - it's not a term I've seen before. If you want to find where f(x)>0 and f(x)<0 then you generally want to find the roots first, values of x such that f(x)=0. Are those 'partition numbers'??
     
  6. Feb 21, 2008 #5
    Sorry about the misunderstanding.

    Yes, partition numbers are values of x such that f(x)=0. So then once I have found those, what should I do in order to find f(x)>0 and f(x)<0?
     
  7. Feb 21, 2008 #6

    Dick

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    Once you've found those, you've found the only places where f(x) can change sign. So if the roots are a<b<c, then f(x) has a constant sign on the intervals x<a, a<x<b, b<x<c and x>c. To figure out what that sign is, just test a point inside each of the intervals.
     
  8. Feb 21, 2008 #7
    ah, okay. Thanks a lot Dick, I appreciate your help!
     
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