Posted by **Carla** on Sunday, December 19, 2010 at 11:15pm.

Find x* on [0, 2] such that f(x*) equals the average value of f(x) = 5x + 9 over [0, 2].

- math question 3- very urgent ! -
**drwls**, Monday, December 20, 2010 at 1:47am
Tha average value of f is the integral of the function (over that [0,2] interval) divided by the interval width, 2.

I assume you know how to integrate the function. The value of the integral is

5/2*4 + 18 = 28 . The average value is therefre 28/2 = 14

Now find what value of x that makes

5x + 9 = 14. It is 1

That should not be a surprise. For a linear function, the average is the value in the middle of the interval.

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