Texas Instruments TI-84 Plus Manual page 56

Press and edit
Y=
Access the statistical lists, clear any previous entries from
, and . Enter the x -values shown above in
L3 L4
and enter
Y1(L1)
Press
ENTER
highlight and type
L3
Press
ENTER
the inputs in
L1
function outputs.
To see what relation the slopes have to the function outputs,
press and highlight
►
It appears that the slope values are a multiple of the function output. In fact, that multiple is ln
2 ≈ 0.693147. Thus we confirm this slope formula: If g ( x ) = 2
4.3.2a CALCULATING
Guide examined the calculator's numerical derivative
gives a good approximation to the slope of the tangent line at points where the instantaneous
rate of change exists. You can also evaluate the calculator's numerical derivative from the
graphics screen using the
it is called dy/dx . We illustrate this use with the function in part a of Example 2 in Section 3.3.
Clear all previously-entered functions in the
= 12.36 + 6.2 ln x in
We want to draw a graph of f . Realize that x > 0 because of
the log term. Choose some value for
ZOOM ▲ [ZoomFit]
With the graph on the screen, press
2ND TRACE (CALC) 6 [dy/dx].
or to move to some point on
◄ ►
the graph. Press
slope of the function is calculated at
the input of this point.
To find the derivative evaluated at a specific value of
could just type in the desired input instead of pressing the arrow
keys. Press
CLEAR 2ND
.
56
to be the function g ( x ) = 2
Y1
. Remember to type
L1
to fill with the function outputs. Then,
L2
Y2(L1).
to fill with the derivative of
L3
. Note that these values are not the same as the
÷
Type
L4. L3
dy
AT SPECIFIC INPUT VALUES The previous two sections of this
dx
menu. However, instead of being named
CALC
.
Y1
Xmax
to set the height of the graph.
Use
and the
ENTER
TRACE (CALC) 6 [dy/dx] 3 ENTER
x
.
,
L1 L2
. Highlight
L1 L2
using
2ND 1 (L1).
evaluated at
Y1
L2 ENTER .
x , then
nDeriv(f(x), x, a)
list. Enter f ( x )
Y=
, say 5. Then use
, you
X
Copyright © Houghton Mifflin Company. All rights reserved.
Chapter 3
,
dg
= (ln 2) 2 x .
dx
and illustrated that it
in that menu,
nDeriv(