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Let f be continuous on [a; b] and differ...

Let f be continuous on `[a; b]` and differentiable on `(a; b)` If `f(x)` is strictly increasing on `(a; b)` then `f'(x) > 0` for all `x in (a; b)` and if `f(x)` is strictly decreasing on `(a; b)` then `f'(x) < 0` for all `x in (a; b)`

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