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# critical points proof question watch

1. let N ( be an element of ) N ( Natural numbers )

P(x)=x(x-1)(x-2)...(x-N+1)

Show that p has ( at least ) N-1 critical poijnts

Any ideas? Thanks
let N ( be an element of ) N ( Natural numbers )

P(x)=x(x-1)(x-2)...(x-N+1)

Show that p has ( at least ) N-1 critical poijnts

Any ideas? Thanks
Looks like Rolle's theorem/MVT will do the job.

(BTW, did you know you can use Latex?: Let )
3. (Original post by atsruser)
Looks like Rolle's theorem/MVT will do the job.

(BTW, did you know you can use Latex?: Let )
Thank you for the response. Doesn't f(a) have to = f(b) to be able to use Rolle's theorm?

ps: I would like to learn LaTeX but haven't found the time to learn the code.
Thank you for the response. Doesn't f(a) have to = f(b) to be able to use Rolle's theorm?
Yes, but here you are looking at the zeros of a polynomial, so so that condition is satisfied.

ps: I would like to learn LaTeX but haven't found the time to learn the code.
It will make your life easier if you do so. And you only have to learn a bit at a time anyway. It's not that tricky to get started.
5. (Original post by atsruser)
Yes, but here you are looking at the zeros of a polynomial, so so that condition is satisfied.

It will make your life easier if you do so. And you only have to learn a bit at a time anyway. It's not that tricky to get started.
I just don't see how I would use Rolle's thm at all. How would I start the proof?
I just don't see how I would use Rolle's thm at all. How would I start the proof?
I'm off to bed now, but:

1. Write down the definition of a critical point.
2. Write down Rolle's Theorem.
3. Think about what has to happen with your function to get a critical point
4. Think about what Rolle's Theorem says about where they will occur
5. Count how many you must therefore have (as a minimum)

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