4
$\begingroup$

Does a continuous function $f$ exist where:

$f$ is continuous,

$f$ is known to be bounded with a codomain of $\left[0,1\right]$

$f''$ (second derivative) is unbounded with a codomain of $(-\infty,+\infty)$

  • 0
    Second line answers the question...2011-05-22
  • 2
    The answer is yes. Have you experimented with examples? To start with, it may help to think of bounded functions with unbounded first derivative. You may want to try sketching their graphs before explicitly defining them.2011-05-22

2 Answers 2