Which of the following statements is true?
1.If $f\in C^\infty$ and $f^{(k)}(0) = 0$ for all integers $k\geq 0$, then $f=0$.
2.$f : [0,\infty] \rightarrow [0,\infty ]$ is continuous and bounded, then $f$ has a fixed point.
for 1 completely out of idea. i tried to find some counter example but could not find it. for 2.this result is true for closed bounded interval.but what is the case here?