MAC 2233/001006 Business Calculus, Fall 2011
CRN: 81700–81702, 81705, 81716, 81715
Name:
Two points
.
Professor
: Stephen Suen
Section:
Peer Leaders
: Hana AboulHosn, Toni Jung, Renan Mendonca
3. Rates of change and derivatives
We encounter rates of change in our everyday life. For example, speed is the rate of change of distance
over time. We shall try to find rates of change graphically and algebraically in this handout.
Example
.
(Rates of change, graphically)
The monthly revenue
R
(in thousands of dollars) of a
bakery store
t
months after its opening is displayed in the chart below.
(a) Estimate the average rate of change of
R
from
t
= 0 to
t
= 3.
Solution.
We find from the graph that
R
= 0 when
t
= 0, and that
R
= 4
.
5 when
t
= 3. Thus average
rate of change of
R
from
t
= 0 to
t
= 3 equals
Δ
R
Δ
t
=
4
.
5

0
3

0
= 0
.
5 thousand dollars per month
.
This shows that the revenue of the store is increasing
on average
at a rate of 500 dollars per month
during the period between
t
= 0 and
t
= 3. We note that this average rate of change equals the slope
of the secant line from
t
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 DANIELYAN
 Calculus, Derivative, Revenue, Toni Jung

Click to edit the document details