Home > Analysis, Olympiad > IMC 2013 Problem 2

IMC 2013 Problem 2


Problem 2. Let {f:\Bbb{R} \rightarrow \Bbb{R}} be a twice differentiable function. Suppose {f(0)=0}. Prove that there exists {\xi \in (-\pi/2,\pi/2)} such that

\displaystyle f''(\xi)=f(\xi)(1+2\tan^2 \xi).

Advertisements
Categories: Analysis, Olympiad Tags: ,
  1. No comments yet.
  1. No trackbacks yet.

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

%d bloggers like this: