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# Ap calc warm up 12.2.13

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### Ap calc warm up 12.2.13

1. 1. Calculus Warm up 12.2.13 Please submit your cumulative review in the bin by the door. Find the average rate of change of f ( x) x 3 9 x 2 on [1,3] Is the function increasing or decreasing on that interval?
2. 2. And now it’s time for.. The Lame Joke of the day.. What do you call an evil pastor? A sinister minister What do you call a cook who can’t hear? A deaf chef What’s another name for the White House? The President’s Residence
3. 3. It is easy to calculate the average value of finitely many numbers y1, y2 , . . . , yn : yave y1 y2 yn n
4. 4. However, how do we compute the average temperature during a day if infinitely many temperature readings are possible?
5. 5. The Mean Value Theorem for Integrals is a consequence of the Mean Value Theorem for derivatives and the Fundamental Theorem of Calculus.
6. 6. • The geometric interpretation of the Mean • Value Theorem for Integrals is as follows. – For ‘positive’ functions f, there is a number c such that the rectangle with base [a, b] and height f(c) has the same area as the region under the graph of f from a to b.
7. 7. Average value of a function The average value of function f on the interval [a, b] is defined as b f ave 1 b a a f ( x)dx Note: For a positive function, we can think of this definition as saying area/width = average height