Calculus Warm up 12.2.13
Please submit your cumulative review in the bin by the door.

Find the average rate of change of ...
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...
It is easy to calculate the average
value of finitely many numbers
y1, y2 , . . . , yn :

yave

y1

y2

yn
n
However, how do we compute the
average temperature during a day if
infinitely many temperature readings
are possible?
The Mean Value Theorem for Integrals
is a consequence of the Mean Value
Theorem for derivatives and the
Fundamental Theore...
• The geometric interpretation of the Mean
• Value Theorem for Integrals is as follows.
– For ‘positive’ functions f, ther...
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 ( ...
Ap calc warm up  12.2.13
Ap calc warm up  12.2.13
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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

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