Polynomial Functions And Models; Finding Second Differences - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
Draw a graph of h with
and use
[Zoom In]
until you are near the point on the graph where x =
If you look closely, you can see the hole in the graph
ENTER .
−
at x = 1. (Note that we are not tracing the graph of h.)
If the view is not magnified enough to
see what is happening around x =
have the cursor near the point on the
curve where x =
to zoom in again.
lim
To estimate
x→
use and
►
close to, and on either side of x =
and observe the sequence of y-values.
Observing the sequence of y-values is the same procedure as numerically estimating the limit at
a point. Therefore, it is not the value at x =
values displayed on the screen approach as x approaches
lim h(x) ≈ 0.43. Therefore, we conclude that
and
+
−
1
x→

1.5 Polynomial Functions and Models

You will in this section learn how to fit functions that have the familiar shape of a parabola or
a cubic to data. Using your calculator to find these equations involves the same procedure as
when using it to fit linear, exponential, log, or logistic functions.

FINDING SECOND DIFFERENCES

use program
DIFF
perfectly quadratic (that is, every data point falls on a quadratic function), the second differ-
ences in the output values are constant. When the second differences are close to constant, a
quadratic function may be appropriate for the data.
We illustrate these ideas with the roofing jobs data given in Table 1.26 of Section 1.5 in
Calculus Concepts. We align the input data so that 1 = January, 2 = February, etc. Clear any
old data and enter these data in lists
Month of the year
Number of roofing jobs
The input values are evenly spaced, so we can see what information is given by viewing the
second differences.
Copyright © Houghton Mifflin Company. All rights reserved.
ZOOM 4 [ZDecimal].
and to move the blinking cursor
◄ ▲
−
1,
−
1 and press
ENTER
h(x), press
TRACE
−
1
to trace the graph
◄
−
1,
to quickly compute second differences in the output values. If the data are
and
L1
1
90
Press
ZOOM 2
−
1. Press
,
−
1 that is important; the limit is what the output
−
1. It appears that
lim h(x) ≈ 0.43.
−
1
x→
When the input values are evenly spaced, you can
L2:
2 3
91 101 120
lim h(x) ≈ 0.43
−
−
1
x→
4 5 6
148 185
39