Texas Instruments TI-82 Manual page 33

symmetric difference) are graphed. You can duplicate this graph by first entering
numerical derivative for Y
2
Figure 2.81: Entering f (x) and f´(x)
Technology Tip: To approximate the second derivative f" (x) of a function y = f( x) or to plot the second derivative,
first enter the expression for Y
pressing MATH 8 2nd Y-
VARS
Figure 2.83 f (x) =
You may also approximate a derivative while you are examining the graph of a function. When you are in a graph
window, press 2nd CALC 6, then use the arrow keys to trace along the curve to a point where you want the
derivative (see figure 2.83 for the graph of f (x) =
for this approximation.
1.11.3 Newton's Method: With your TI-82, you may iterate using Newton's method to find the zeros of a function.
Recall that Newton's Method determines each successive approximation by the formula
As an example of the technique, consider f (x) = 2x
suggests that it has a zero near x = –1, so start the iteration by going to the home screen and storing –1 as x (see
figure 2.85). Then press these keystrokes:
STO► . Press ENTER repeatedly until two successive approximations differ by less than some predetermined
X,T,θ
value, say 0.0001. Note that each time you press ENTER, the TI-82 will use its current value of x, and that value is
changing as you continue the iteration.
33
G T
RAPHING ECHNOLOGY
by pressing MATH 8 2nd Y-
and its derivative for Y
1 2
1 2, , ).
X,T,θ X,T,θ
−
5 x 2
at x = –2.3
2 +
x 1
−
5 x 2
2 +
x 1
3
+ x
– 2nd Y-
X,T,θ
Copyright © Houghton Mifflin Company. All rights reserved.
G : TI-82
UIDE
5 x
x
1 1 , , ) as you see in Figure 2.81.
VARS X,T,θ X,T,θ
Figure 2.82: Graphs of f (x) and f´(x)
as above. Then enter the second derivative for Y
Figure 2.84: dy/dx
at x = –2.3) and press ENTER. The TI-82 uses ∆x = 0.001
2
– x + 1. Enter this function as Y
1 1 ÷ MATH 8 2nd Y-
VARS
−
2
for Y and then entering its
1
+
2
1
by
3
f x ( )
= −
n
x x .
+
n 1 n '
f x ( )
n
. A look at its graph
1
1 1 , , )
VARS X,T,θ X,T,θ