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Partition Numbers

by undrcvrbro
Tags: numbers, partition
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undrcvrbro
#1
Feb21-08, 03:27 PM
P: 138
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?
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Dick
#2
Feb21-08, 03:30 PM
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What are the 'partition numbers' of a function f(x)?? Can you define that??
undrcvrbro
#3
Feb21-08, 03:33 PM
P: 138
brain fart. I'm a little flooded in work and lacking sleep..sorry.

the function is f(x)=x^3-3x^2-2x+5

Dick
#4
Feb21-08, 03:51 PM
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Partition Numbers

Quote Quote by undrcvrbro View Post
brain fart. I'm a little flooded in work and lacking sleep..sorry.

the function is f(x)=x^3-3x^2-2x+5
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'??
undrcvrbro
#5
Feb21-08, 04:04 PM
P: 138
Quote Quote by Dick View Post
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'??
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?
Dick
#6
Feb21-08, 04:10 PM
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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.
undrcvrbro
#7
Feb21-08, 05:22 PM
P: 138
ah, okay. Thanks a lot Dick, I appreciate your help!


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