Visualizing And Estimating Rates Of Change Of Cross Sections - Texas Instruments TI-84 Plus Manual

NOTE: You may find it helpful to place a piece of paper or a ruler under the row (or to the
right of the column) in which the data appear to help avoid entering an incorrect value.
You can reuse the input data from Ex.
1 of Section 9.3 and enter the output
in L2., Next, clear any functions
from the list, and turn on
Y=
Draw a scatter plot of the data with
ZOOM 9 [ZoomStat].
There is an inflection point and no
evidence of limiting values, so the
data appear to be cubic. Fit a cubic
function and copy it to the
Draw the cubic function on the scatter
plot with
GRAPH

VISUALIZING AND ESTIMATING RATES OF CHANGE OF CROSS SECTIONS

The rate of change of a multivariable function (when evaluated at a specific point) is the slope
of the line tangent to the graph of a cross-sectional function at that point. We illustrate this
concept in this section and the next using the Missouri farmland cross-section equations for
elevation: E (0.8, n ) and E ( e, 0.6). It would be best to use the unrounded functions that were
found in the previous example of this Guide . However, to illustrate the rate-of-change
techniques, we use the rounded functions rather than re-enter all the data.
−
2
Enter 2.5 n + 2.497 n + 799.490 =
E (0.8, n ) in . Because we are going
Y1
to graph this function, use
the input variable.
Press
WINDOW
as those shown to the right.
The window settings used above can be obtained by drawing a scatter plot of the data used to
find E (0.8, n ) or by looking at the e = 0.8 column in Table 9.3 in Calculus Concepts . The line
tangent to the graph at n =
screen. (See p. 46 of this Guide for an explanation of both methods.) We use the home screen
method in this section and the graphics screen method in the next.
Press
GRAPH
Return to the home screen. Press
Y1.
2ND
PRGM (DRAW) 5 [Tangent(]
VARS ► [Y−VARS] 1 [Function] 1
[Y1] , . 6 ) .
100
.
Plot1
list.
Y=
.
, not n , as
X
and set values such
= 0.6 can be drawn from either the home screen or the graphics
X
to draw the graph of
This command draws the
line tangent to E(0.8, n) =
Y1 at n = 0.6.
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 9
Press ENTER to see
the tangent line.