# question

• April 9th 2013, 12:32 PM
orir
question
f(x) is a continous function in R.
i need to prove that if f(x)>=x2 for every x at R, so f(X) gets a minimum at [0,infinty).

thanks!
• April 9th 2013, 02:03 PM
Plato
Re: question
Quote:

Originally Posted by orir
f(x) is a continous function in R.
i need to prove that if f(x)>=x2 for every x at R, so f(X) gets a minimum at [0,infinty).

It is not true: $f(x) = \left\{ {\begin{array}{*{20}{rl}} {1,}&{\left| x \right| \leqslant 1} \\ {\left| {{x^3}} \right|,}&\text{else} \end{array}} \right.$
• April 11th 2013, 11:53 AM
orir
Re: question
but isn't it still a minimum?
after all, still f(x0)<=f(x) [for every x at [0,infinity)]

or not?
• April 11th 2013, 12:02 PM
Plato
Re: question
Quote:

Originally Posted by orir
but isn't it still a minimum?
after all, still f(x0)<=f(x) [for every x at [0,infinity)]

Again, this may be a translation difficulty.
What does "f(X) gets a minimum at [0,infinty)" mean?

The function I gave you does have a minimum at every point in $[-1,1]$, but on others.