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Section 6.5 Average Value of a Function

Section 6.5 Average Value of a Function. AP Calculus December 11, 2009 Berkley High School todd1@toddfadoir.com. What does average mean?. What is the average of the function f(x)=4 ? Obviously, the average is 4. Could it also be the area divided by the width?. What does average mean?.

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Section 6.5 Average Value of a Function

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  1. Section 6.5Average Value of a Function AP Calculus December 11, 2009 Berkley High School todd1@toddfadoir.com

  2. What does average mean? • What is the average of the function f(x)=4? • Obviously, the average is 4. • Could it also be the area divided by the width? Calculus, Section 6.5, Todd Fadoir, CASA, 2003

  3. What does average mean? • What is the average of the function f(x)=.5x from 0 to 8? • What the area under the curve? • 16 units2 • What is the average? • 16/8=2 units Calculus, Section 6.5, Todd Fadoir, CASA, 2003

  4. Average value of f Calculus, Section 6.5, Todd Fadoir, CASA, 2003

  5. What does average mean? • What is the average of the function f(x)=-.25x*(x-8)from 0 to 8? Calculus, Section 6.5, Todd Fadoir, CASA, 2003

  6. Example • What is the average value of sin(x) on the interval [π/2,π]? Calculus, Section 6.5, Todd Fadoir, CASA, 2003

  7. Mean Value Theorem for Integrals Calculus, Section 6.5, Todd Fadoir, CASA, 2003

  8. Example • What value(s) c satisfy the MVT for integrals for sin(x) on the interval [π/2,π]? Calculus, Section 6.5, Todd Fadoir, CASA, 2003

  9. Assignment • Section 6.5, 1-15, odd Calculus, Section 6.5, Todd Fadoir, CASA, 2003

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