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.
4 is in the closed interval (1, 6)
The mean-value theorem is satisfied.