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The Mean Value Theorem for Integrals – Average Value
Just as mean as before The Mean Value Theorem for Integrals – Average Value Lesson 5.7
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Average Value of a Function
Consider recording a temperature each hour and taking an average If we take it more often and take a limit …
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Average Value of a Function
Now apply the concept to a continuous function f(x) is the height of the "box" which is equal to the area under the curve. a b
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Average Value of a Function
Find the average value of these functions
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Finding Where This Happens
This height will be f(c) for some x = c (at least 1) And we can solve for that value of c f(x) a b c
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Try It Out Given f(x) = x2 + 4x +1 on [0, 2]
Find a value for c such that
![Try It Out Given f(x) = x2 + 4x +1 on [0, 2]](http://slideplayer.com/slide/14044136/86/images/6/Try+It+Out+Given+f%28x%29+%3D+x2+%2B+4x+%2B1+on+%5B0%2C+2%5D.jpg "Find a value for c such that.")
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Application Suppose a study comes up with a model that says t years from now CO2 in the area of a city will be What is the average level in the first 3 years? At what point in time does that average level actually occur
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Assignment Lesson 5.7 Page 332 Exercises 1 – 35 odd
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