The diagram shows a door with an automatic
closer. At time t = 0 seconds someone pushes the
door. It swings open, slows down, stops, starts
closing, then slams shut at time t = 7 seconds. As
the door is in motion the number of degrees, d, it
is from its closed position depends on t.
1.
Sketch a reasonable graph of d versus t.
2.
Suppose that d is given by the equation
d
=
200t
•
2

t
.
Plot this graph on your calculator. Sketch
the results here.
3.
Make a table of values of d for each
second from t = 0 through t = 10. Round
to the nearest 0.1˚.
4.
At time t = 1 second, does the door appear
to be opening or closing? How do you
tell?
5.
What is the average rate at which the door
is moving for the time interval [1, 1.1]?
Based on your answer, does the door
seem to be opening or closing at time t =
1? Explain.
6.
Find an estimate of the instantaneous rate
at which the door is moving at time t = 1
second. Show how you get your answer.
7.
In calculus you will learn by four methods:
• algebraically,
• numerically,
• graphically,
• verbally (talking and writing).
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.
 Spring '08
 Grether
 Rate Of Change, instantaneous rate

Click to edit the document details