1. AP Calculus March 31, 2017 Mrs. Agnew
Average Value
AP Calculus
March 31, 2017
Mrs. Agnew

2. Essential Question Essential Vocabulary
How do you find the average value of a function?
Essential Vocabulary
Average Value
Mean Value Theorem
Integral

3. Average Value
How do you find average value of a finite number of values?
What if we had an infinite number of values?
Example: Average temperature for the day given infinitely many readings.

4. Mean Value Theorem
If f is continuous over [a,b], then there exists a number c in the interval [a,b] such that…
Geometric Interpretation
Animation and Examples (Larson)

5. Mean Value Theorem Mean Value Theorem is an existence theorem.
The mean value for definite integrals is also known as the average value of the function.

6. Average Value
Given f is integrable over [a,b], then the average value of f over the interval is…
Practice
Average Value Examples (Larson)

7. (for #5 – 8, only do parts a & b)
Homework: 3/31/17
Page #1 – 11, 13
(for #5 – 8, only do parts a & b)