What is the smallest n for which...

On my latest assignment in high school calculus to do over the Spring Break, I've been given this problem: "What is the smallest n for which d^n(12x^3 + 2x) / dx^n = 0, for all x?" - I don't know where to start with this, but my teacher mentioned something about finding the derivatives. Can someone here please help point me in the right direction?

Re: What is the smallest n for which...

Well, find , , , ... and see when it becomes 0. Of course, you need to know what the definition of is.

Re: What is the smallest n for which...

Quote:

Originally Posted by

**emakarov** Well, find

,

,

, ... and see when it becomes 0. Of course, you need to know what the definition of

is.

Now that you write it out like that, I now know exactly what the "d^n / dx^n" part meant and was able to solve the problem easily. Thanks!