Math Is Fun Forum

wcy

Member

Registered: 2005-08-04

Posts: 117

nth derivative (needs computer help)

Hi, can anyone help to solve this very challenging problem?

(needs computer help on this)

I tried using many programs but all failed..

the small number (2) is a hint to try x, x^2, and x^3 first and guess the pattern

Last edited by wcy (2009-09-16 16:50:16)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: nth derivative (needs computer help)

Hi wcy;

Working a little bit on your problem, I was able to shorten it to:

Testing up to f ^(50) (0) produced only zeros. Perhaps you should be trying to prove that for all n = 1,2,3 ... f^(n)(0) = 0.

Last edited by bobbym (2009-09-16 19:35:10)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

wcy

Member

Registered: 2005-08-04

Posts: 117

Re: nth derivative (needs computer help)

thanks a lot bobbym
i tried using Maple software in my school, and working on the hint, I suspect the answer is 2009x3=18081.

(the hint is try on x, x^2, and x^3 first and guess for 2009)
By the way, which program did u use to test up to f^50?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: nth derivative (needs computer help)

Hi wcy;

Mathematica, can you tell me why you think n = 9 * 2009 = 18081 is the answer.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

wcy

Member

Registered: 2005-08-04

Posts: 117

Re: nth derivative (needs computer help)

oh its actually because using
(the hint is try on x, x^2, and x^3 first and guess for 2009)
we obtain
9, 18, 27 respectively, suggesting that the number is the 2009th multiple of 9

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: nth derivative (needs computer help)

Hi wcy;

That is an interesting conjecture( and I have verified it).  Assuming that:

x power  derivative

1             9
2             18
3             27

9*(xpower) = derivative is indeed the simplest fit and in physics we look for the simplest answer, but in math that doesn't hold. There are other relationships for (1,9),(2,18),(3,27) that may be the correct answer. Also that pattern may not continue, the next one might be 112.

Last edited by bobbym (2009-09-24 21:41:50)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.