Partition Numbers: Approximating & Solving Inequalities

[undrcvrbro]

Homework Statement

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

Homework Equations

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?

 

[Dick]

What are the 'partition numbers' of a function f(x)?? Can you define that??

 

[undrcvrbro]

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

 

[Dick]

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]

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]

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]

ah, okay. Thanks a lot Dick, I appreciate your help!