Where to start I need to multiply and divide by somthing anyone c it?

  • Thread starter mr_coffee
  • Start date
In summary, the conversation revolves around a problem that requires showing the equality of two sides using the mean value theorem or the chain rule. The problem is to prove that (f(p) - f(a))/(p-a) = (f(p) - f(a))/(h(p) - h(a)) * (h(p) - h(a))/(p-a), and the discussion includes different approaches to solving it, with the conclusion that using the mean value theorem or the chain rule is the most efficient method.
  • #1
mr_coffee
1,629
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Hello everyone, I'm really lost on this problem, am i proving like the chain rule or composition of functions? Here is the problem:
http://img499.imageshack.us/img499/3791/lastscan6ya.jpg [Broken]
or here:
http://show.imagehosting.us/show/921262/0/nouser_921/T0_-1_921262.jpg

THe professor told me to multiply and dvide by the right thing which didn't help much. I started to multiply
(h(p)-h(a))/(p-a) through and it just got really ugly, I don't see how this is going to work at all! Any tips on how I can get this started? :bugeye:
 
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  • #2
Am I missing something? You are asked to show that
[tex]\frac{f(p)-f(a)}{p-a}= \frac{f(p)-f(a)}{h(p)-h(a)}\frac{h(p)-h(a)}{p-a}[/tex]
Isn't that obvious? You multiply and divide the left hand side by h(p)- h(a)!

Or are you missing the fact that f(p)-f(a)= g(h(p))- g(h(a)) by definition of f?
 
  • #3
wait you are right...what the heck, i didn't even look at the left hand side, i figured I should try and make the right hand side equal to the left but that is so easy to prove the left is equal to the right by doing waht you said. How is this going to prove anything? it seems so easy to just do that, is that it?
 
  • #4
can someone tell me what I'm trying to prove? is it the chain rule? this will help me find out where I'm suppose to go with this.
 
  • #5
It kinda looks like some kind of application of the mean value theorem to me.

Why not use the mean value theorem:

(f(p) - f(a))/(p-a) = f`(some value c between p and a)

for it to work, you only have to take the derivative of g(h(c)).
 
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  • #6
Will that show what he is asking? I think he wants me to keep it in the forum of the given information of the problem, but I like your idea.
 
  • #7
mr_coffee said:
Will that show what he is asking? I think he wants me to keep it in the forum of the given information of the problem, but I like your idea.

I can't answer "Will that show what he is asking?" since I have no idea who "he" is! It looks to me as if you are doing part of the proof of the mean value theorem.
 
  • #8
THanks for the responce, all he wants is what hte problem wants, is to just show that one side is equal to the other, it seems like you already told me how to do that. It just seems so simplistic.
 
  • #9
Thanks for the help everyone, Hall was right on the proof. It also wasn't proving the mean value, it was proving the chain rule if anyone cares.
 

1. What is the first step in multiplying and dividing?

The first step in multiplying and dividing is to identify the numbers that you need to multiply or divide. These are called the factors.

2. How do I decide which operation to use?

To decide whether to multiply or divide, you need to look at the problem and determine what the problem is asking for. If the problem is asking you to find the total of equal groups, you should use multiplication. If the problem is asking you to divide a total into equal groups, you should use division.

3. Can I use any number to multiply or divide?

Yes, you can use any number to multiply or divide. However, it is important to remember that when you multiply or divide by a number, you are essentially making the number bigger or smaller. So, it is important to choose numbers that make sense in the context of the problem.

4. What is the difference between multiplying and dividing?

Multiplying is the process of finding the total of equal groups, while dividing is the process of dividing a total into equal groups. In multiplication, the answer is the total, while in division, the answer is the number of groups.

5. Are there any tricks to help me with multiplying and dividing?

Yes, there are some tricks that can help you with multiplying and dividing. For example, you can use skip counting to quickly find the answer to a multiplication problem. You can also use the distributive property to break down a larger multiplication problem into smaller, easier ones. Additionally, you can use inverse operations to check your answers when dividing.

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