- #1
Kruger
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Homework Statement
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.
Homework Equations
-> The mathematical definition of continuous and limes
(but I really don't know if these are needed)
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.