Finding Rates Of Change Using Cross-Sectional Models - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
You can obtain an estimate of the tan-
gent line slope with 2ND
(CALC) 6 [dy/dx].
move the cursor as close as possible to
n = = 0.6. Press
X
We could have obtained a much better estimate than the one given above if we had found the
slope of the tangent line at
allows you to do this on the home screen or graphically. Here we illustrate the graphical
method.
Have E (0.8, n ), using X as the input variable, in
tangent line to E (0.8, n ) at n = 0.6 by first drawing the graph of
the function with
2ND
PRGM (DRAW) 5 [Tangent(] . 6 ENTER .
Because this method gives the equation of the line tangent to the graph at the chosen input,
you can see that the slope of the tangent,
FINDING RATES OF CHANGE USING CROSS-SECTIONAL MODELS The methods
described in the last section require that you use
The process of replacing other variables with
this replacement when you use the calculator numerical derivative on the home screen to
evaluate rates of change at specific input values. We illustrate with the cross-sectional function
−
E ( e, 0.6) = 10.124 e
Section 9.2.1b of this Guide . We also demonstrate this method with the cross-section E (0.8, n )
that was found in Section 9.2.1a and used on page 100 of this Guide .
NOTE: Whenever possible, you should use the complete equation found by the calculator with
this method. However, to avoid re-entering the data, we use the rounded functions to illustrate.
Have E (0.8, n ) =
variable, in
Y1
.
Y2
(Remember that because we are not using
variable, we should not draw a graph or use the
NOTE: These functions could be entered on the home screen instead of in the
use and
Y1 Y2
Tell the calculator the point at which
the derivative is to be evaluated by
storing the values. Then, on the home
dE
screen, find
0.6 with the numerical derivative
nDeriv.
Copyright © Houghton Mifflin Company. All rights reserved.
TRACE
Use or to
► ◄
ENTER .
= 0.6 rather than a value close to that number. The calculator
X
With the graph on the screen, press
GRAPH .
3 + 21.347 e 2 – 13.972 e + 802.809 feet above sea level that was found in
−
2.5 n 2 + 2.497 n + 799.490, using
. Enter E ( e, 0.6), using
in the list because they are convenient locations to hold the equations.
Y=
( 0 8 . , )
n
evaluated at n =
dn
0.6 is not a trace value.
. Draw the
Y1
( 0 8 . , )
dE n
at n = 0.6, is about
dn
as the input variable to find rates of change.
X
can be confusing. You can avoid having to do
X
as the input
N
as the input variable, in
E
as the input
X
TABLE.)
This is just an estimate.
−
0.503 foot/mile.
list. We
Y=
101