(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a continuous function f(x):R->R with

lim(f(x)/x^2)=0, x-->+-infinity

Show that then an element t exist such that:

x^2+f(x)>=t^2+f(t) for every x in R.

2. Relevant equations

-> The mathematical definition of continuous and limes

(but I really don't know if these are needed)

3. The attempt at a solution

I really thought hours on that problem but didn't find a solution. I've no really good attempt. Well, I know that f(x) has to increase less rapidly than x^2 accordint to lim(f(x)/x^2)=0, x-->+-infinity.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Function inequality

**Physics Forums | Science Articles, Homework Help, Discussion**