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The Average Value of a Function

The Average Value of a Function. 30.

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The Average Value of a Function

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  1. The Average Value of a Function

  2. 30 Example 1: Find the average of 10, 20 and 60. _______ Just as we find the average of numbers by adding their values and dividing by the number of values, we can find the average (y-)value of a function by adding the y-values together (or ______________________ ) and dividing by the number of y-values (the______________ of the interval). Integrating Length

  3. If f is integrable on [a, b], the average value of f=

  4. Example 2: Find the average value of

  5. The Mean Value Theorem for Definite Integrals

  6. If f is continuous on [a, b], then at some point c in [a, b],

  7. Example 3: Find the value of c for which the MVT for definite integrals is true for example 2.

  8. Homework (on back of 5.4 Worksheet)NO FNINT ON CALCULATOR!!!!1. Find the value of c guaranteed by the Mean Value Theorem for f(x) = x3 on [0, 2].2. Find the average value on the interval [-2, 2] of f(x) = 4-x2

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