One On One

If $F(x): \mathbb R \to \mathbb R$ is a one-to-one continuous and differentiable function then which of the following is always true?

(1) : $F'(x)$ must be strictly decreasing or strictly increasing for all $x$ .
(2) : $F'(x)$ can be equal to 0 for some continuous domain of $x$ .
(3) : $F'(x)$ can be equal to 0 for some discrete values of $x$ .

Notation : $\mathbb R$ denotes the set of real numbers .