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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