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?
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
It is easy to calculate the average
value of finitely many numbers
y1, y2 , . . . , yn :
However, how do we compute the
average temperature during a day if
infinitely many temperature readings
The Mean Value Theorem for Integrals
is a consequence of the Mean Value
Theorem for derivatives and the
Fundamental Theorem of Calculus.
• 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.
Average value of a function
The average value of function f on the interval [a, b] is
f ( x)dx
Note: For a positive function, we can think of this
definition as saying area/width = average height