The Chain Rule; Summary Of Checking Methods - Texas Instruments TI-84 Plus Manual

Start with
ZOOM 4 [ZDecimal] or ZOOM 6 [ZStandard].
of these shows a graph (because of the large coefficient in the
function), but you can press
values. Using those values, reset the window. The graph to the
right was drawn in the window [
any view that shows the graph will do.
Now, press
Y= ,
holds the formula for the derivative of
numerically by the calculator.) Press
are drawing the graph of
you graphed
Y2
If you see the same graph, your algebraic formula (in

3.4 The Chain Rule

You probably noticed that checking your answer for a slope formula graphically is more diffi-
cult than checking your answer using the table if you have to spend a lot of time finding a
window in which to view the graph. Practice with these methods will help you determine
which is the best to use to check your answer. (These ideas also apply to Section 3.5.)
SUMMARY OF CHECKING METHODS Before you begin checking your answer, make
sure that you have correctly entered the function. It is very frustrating to miss the answer to a
problem because you have made an error in entering a function in your calculator. We sum-
marize the methods of checking your algebraic answer using the function in Example 3 of
Section 3.4 of Calculus Concepts.
Enter the function P(t) =
your answer for P
. Turn off
Y3 Y1
Go to the table, which has been set to
3 input values. (Because this problem is in a context, read the
problem to see which inputs make sense.)
It seems that the answer in
If you prefer a graphical check, the problem states that the equa-
tion is valid between 1980 and 2001 (and the input is the number
of years after 1980). So, turn off
and draw a graph of
window, draw a graph of
the same, again suggesting a correct answer in
58
to see some of the output
TRACE
−
10, 10] by [0.331, 0.545], but
turn off and turn on
Y2
Y1
GRAPH .
in exactly the same window in which
Y3
.
84 4
.
−
0 484
.
+
1 33 6
. e
'
in , and the CALCULATOR derivative in
Y2
.
ASK
is probably correct.
Y2
, set
Y3
using
Y2 ZoomFit.
with turned off. The graphs are
Y3 Y2
Neither
. Recall that
Y3 ( Y3
as computed
Note that you
) is very likely correct.
Y2
in the location,
Y1
t
mode. Enter at least
, ,
Xmin = 0 Xmax = 21
Then, using the same
.
Y2
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 3