Find a continuous and bounded function on $[0,\infty)$ where the extreme value theorem does not hold. Find a continuous and bounded function on $[0,\infty)$ where the extreme value theorem does not hold.
I think I may need to use the Balzono-Weierstrass Theorem for this problem but I'm having trouble getting started.

f := [0, $\infty$) $\rightarrow$ [0, 1)
f(x) = $x^2 \over{x^2+1}$ 
