Average Value of a Function

1. Average Value of a Function
A REVIEW FOR YOU 

3. How did we find
averages in
elementary
school?
WE ADDED UP ALL OF OUR
NUMBERS, AND THEN DIVIDED
BY HOWEVER MANY NUMBERS
WE ADDED!

4. We can also find
the average value
of a function.
BUT A FUNCTION HAS
INFINITELY MANY VALUES ON
A CLOSED INTERVAL. SO…

5. We can use an integral!!!
YAY!!!

6. Average Value of a
Function

1
𝑏−𝑎 𝑎
𝑏
𝑓 𝑥 𝑑𝑥
-f(x) is continuous on
[a, b]
-f(x) is differentiable
on (a, b)

7. Try this example in your notes. Then, move to
the next slide to check your answer.
 Calculate the average value of 𝑓 𝑥 = 𝑒 𝑥
on
[1, 4].

8. How did you do? 

1
4−1 1
4
𝑒 𝑥
𝑑𝑥
 =
1
3
𝑒 𝑥 4
1
 =
1
3
𝑒4
− 𝑒1
 =
𝑒4−𝑒
3