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8.4 Mean Value

If y = f (x) is given a function defined on [a, b], then the mean value of the function denoted by y = f (c) is defined as y or f (c) = for some c Î (a, b)

Example 27 Find the mean value of y = over [0, 2]

Solution : By Mean value theorem

The mean value theorem is also satisfied.

Example 28 Given that = 318 Find the mean value of x3 - 1 and also find all 'c' values that satisfies the mean value theorem for this function on the closed interval.

Solution :

\ c » 4 is in the closed interval (1, 6)

\ The mean-value theorem is satisfied.

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Index

8.1 Introduction
8.2 Area
8.3 Volumes
8.4 Mean Value
8.5 Arc Length(Rectification)

Chapter 1

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