Texas Instruments TI-85 - Section 5.2 in Text: Numerical Derivatives; nDeriv for First Derivatives

Section 3.3 in Text
• nDeriv
• NDERG
nDeriv
Find nDeriv p(2), the numerical derivative, where
p(x) = 1/x. Refer to Examples 2 and 3 and Explo-
ratio 1 in the text.
Solution. To find nDeriv p(2), use the built-in nDeriv
function on your TI-82. Press
MATH 8 and you will
see nDeriv( on the screen. Now press the keys
1 ÷ X,T,θ
,
X,T,θ
,
2 ) ENTER
and obtain
Your answer is −.2500000625.
NDERG
nDERG draws a graph of the numerical derivative. Use
NDERG for f(x) = x
1/3
.
Solution. No programming is required for NDERG
on the TI-82, just use the built-in nDeriv program. Set
Y
1
= nDeriv(X
(1/3)
,X,X) and graph using a window
with dimensions [0, 1] by [0, 10].
Section 5.2 in Text
• nDer2
• NDER2G
nDer2
nDer2 gives a numerical second derivative. Find
nDer2f(1) if f(x) = x
4
.
Solution. To find nDer2f (1), input Y
1
= x
4
and ex-
ecute the program NDER2. The program asks for c.
Input 1 and press the ENTER key. The program re-
turns 12.000008.
NDER2G
NDER2G graphs a numerical second derivative. With
f(x) = x
4
use NDER2G to obtain a graph of y =
nDerf(x).
Solution. Input Y
1
= x
4
and use a window with
dimensions [0, 1] by [0, 12]. Execute the program
NDER2G and you obtain the following
Section 6.3 in Text
• The Program RECT
• The Program SUM
The Program RECT
The program RECT draws the graph of a function,
the rectangles associated with the left- and right-hand
sums, and the values of these sums. Obtain the left-
and right-hand sums for y = x
2
and n = 5. (You will
obtain Figures 6.7 in the text.)
Solution. First input Y
1
= x
2
and then set the di-
mensions of the window to [0, 1] by [0, 1]. Execute the
program RECT. A value of n is requested. Press
5
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