# One On One

Calculus Level 4

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.

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