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Mean Value Theorem
MEAN VALUE THEOREM Assume that f is continuous on the closed interval [a, b] and has a derivative at every point of the open interval (a, b). Then there is at least one point c in (a, b) where the slope f'(c) is equal to the average slope of f between a and b,
Remark In the special case that f(a) = f(b) = 0, the Mean Value Theorem becomes Rolle's Theorem:
On the other hand, we shall use Rolle's Theorem in the proof of the Mean Value Theorem. The Mean Value Theorem is illustrated in Figure 3.8.18.
Figure 3.8.18 The Mean Value Theorem
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Last Update: 2006-11-05