Mean Value Theorem for Integrals
If f is continuous on the closed interval [a, b], then
there exists a number c in the closed interval [a, b]
such that:
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Average Value of a Function on an Interval
If f is integrable on the closed interval [a,b], then the average
value of f on the interval is:
*Note: The area of the region under the graph of f is equal to
the area of the rectangle whose height is the average value of f.
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I thought that to find the "average value" you
found the slope? Why is this different?
*If you are asked to find the average value of
the derivative of a function, you find the slope
(i.e. you are given position and are asked to
find the average velocity)
*If you are asked to find the average value of
the function you are given, you do
(i.e. you are given velocity and are asked to
find average velocity)
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Ex 2. Find all values of c guaranteed by the Mean Value
Theorem for Integrals for the function
f(x) = 3x2 - 2x on the interval [1, 4].
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Homework:
pg. 291,
#s 15-18, 31, 32 (w/ calc.),35, 36
pg. 293 (Quick Quiz),
#s 1-4
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