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Math and science::Analysis::Tao::10: Differentiation of functions

Derivative of monotone functions

Monotone increasing implies [...]

Let \( X \) be a subset of \( \mathbb{R} \), and let \( x_0 \in X \) be a limit point of \( X \). Let \( f: X \to \mathbb{R} \) be a function. If \( f \) is [...] and is [...], then \( f'(x_0) \ge 0 \).

If instead, \( f \) is monotone decreasing, then \( f'(x_0) \le 0 \).