  It is well known that a continuously differentiable function is monotone in
an interval $[a,b]$ if and only if its first derivative does not change its
sign there. We prove that this is equivalent to requiring that the Caputo
derivatives of all orders $\alpha \in (0,1)$ with starting point $a$ of this
function do not have a change of sign there. In contrast to what is
occasionally conjectured, it not sufficient if the Caputo derivatives have a
constant sign for a few values of $\alpha \in (0,1)$ only.
