Theorem 4.13. Suppose that f is continuous on the closed interval I and has a derivative at each point of I₁, the interior of I. 88 f(a)| y = f(x) slope = f'(E) 1 1 | f(b) 1 b (a) If f' is positive on I₁, then f is increasing on I. (b) Iff' is negative on I₁, then f is decreasing on I. X Figure 4.4. Illustrating the Mean-value theorem. 4. Elementary Theory of Differentiation

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