Sufficient Condition to be a Polynomial?

Appropriate Level:  Real analysis.

The Question:  Suppose f: \mathbb{R} \rightarrow \mathbb{R} is infinitely differentiable and that for each x \in \mathbb{R} there is some n \in \mathbb{N} for which the n-th derivative of f at x equals 0.  Must f be a polynomial?

 

Advertisements

About Aaron

I like good math problems.
This entry was posted in Uncategorized. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s