Texas Instruments TI-84 Plus Manual page 63

TI-83, TI-83 Plus, TI-84 Plus Guide
Enter f in the
in , and the second derivative of f in
Y2
round any decimal values.)
Turn off and
Y1
We are given the input interval 1982 through 1990, so 0 ≤ x ≤ 8.
Either use
ZoomFit
− 4 ≤ y ≤ 4. Because we are looking for the x-intercept(s)
We use
of the second derivative graph, any view that shows the line
crossing the horizontal axis is okay to use.
Use the methods indicated on pages 61 and 62 of this Guide to
find where the second derivative graph crosses the x-axis.
(Note that when you are asked for the inflection point of f, give
both the input and an output of the original function.)
Return to the home screen and enter
just found as the x-intercept remains stored in the
until you change it by tracing, using the
Find the y-value by substituting this x-value into
At some point, be sure to examine a graph of the function and
verify that an inflection point does occur at the point you have
found. To do this, turn off
draw the graph. Trace near where x ≈ 4.27 and y ≈ 51.6. The
graph of R confirms that an inflection point occurs at this point.
•
The calculator will usually draw an accurate graph of the first derivative of a function
when you use
calculate or graph f
f '
nDeriv( , X, X)
down" and gives invalid results. If this should occur, the graph of
very jagged and this method should not be used.
Enter f in the
in , and the second derivative of f in
Y2
calculator's numerical derivative for each derivative that you
enter.
Turn off
Y1.
problem directions indicate.)
Draw the graph of the first derivative
derivative
(Y3)
to set the vertical view or experiment until you find a
ZoomFit
suitable view. The graph to the right uses
Copyright © Houghton Mifflin Company. All rights reserved.
location of the list, the first derivative of f
Y1 Y=
Y2.
or choose some appropriate vertical view.
, turn on
Y3
However, this calculator does not have a built-in method to
nDeriv(.
''
, the second derivative. As illustrated below, you can try to use
''
to find f . Be cautioned, however, that
location of the list, the first derivative of f
Y1 Y=
Be sure that and
Xmin = 0
of f using an appropriate window. You can use
. (Be careful not to
Y3
. The x-value you
X,T,θ,n
location
X
, and so forth.
SOLVER
.
Y1
, and use to
Y1 ZoomFit
nDeriv(
, using the
Y3
(as the
Xmax = 8
and the second
(Y2)
− 4 ≤ y ≤ 4.
f '
sometimes "breaks
, X, X)
f '
appears
nDeriv( , X, X)
63