Numerically Checking Slope Formulas; Graphically Checking Slope Formulas - Texas Instruments TI-84 Plus Manual

TI-83, TI-83 Plus, TI-84 Plus Guide
The slope
dy/dx = 2.0666667
Return to the home screen and press
memory location has been updated to 3. Now type the
X
numerical derivative instruction (evaluated at 3) as shown to the
right. This is the dy/dx value you saw on the graphics screen.
You can use the ideas presented above to check your algebraic formula for the derivative. We
next investigate this procedure.

NUMERICALLY CHECKING SLOPE FORMULAS

your answer. Although your calculator cannot give you an algebraic formula for the derivative
function, you can use numerical techniques to check your algebraic derivative formula. The
basic idea of the checking process is that if you evaluate your derivative and the calculator's
numerical derivative at several randomly chosen values of the input variable and the outputs
are basically the same values, your derivative is probably correct.
These same procedures are applicable when you check your results (in the next several
sections) after applying the Sum Rule, the Chain Rule, or the Product Rule. We use the fun-
ction in part c of Example 2 in Section 3.3 of Calculus Concepts to illustrate.
Enter m ( r ) =
Compute m'(r) using pencil and paper and the derivative rules.
Enter this function in
not be the same as what appears to the right.)
Enter the calculator's numerical derivative of
general input
if the outputs of
Press
2ND
location. Access the table with
Indpnt:
and delete or type over any previous entries in the
Enter at least three different values for
The table gives strong evidence that that
GRAPHICALLY CHECKING SLOPE FORMULAS When it is used correctly, a graphi-
cal check of your algebraic formula works well because you can look at many more inputs
when drawing a graph than when viewing specific inputs in a table. We illustrate this use with
the function in part d of Example 2 in Section 3.3 of Calculus Concepts.
Enter j(y) =
17 1
Next, using pencil and paper and the derivative rules, compute
'
(y). Enter this function in
j
Enter the calculator's numerical derivative of
general input
of and .
Y1 Y3
To graphically check your derivative formula answer, you now need to find a good graph of
. Because this function is not in a context with a given input interval, the time it takes to
Y2
find a graph is shortened if you know the approximate shape of the graph. Note that the graph
of the function in
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appears at the bottom of the screen.
8
−
12 in (using
Y1 X
r
r
. (What you enter in
Y2
) in Because you are interested in seeing
X Y3.
and are the same, turn off
Y2 Y3
and choose
WINDOW (TBLSET)
( )
12
y
+
0.025 in using
Y1,
12
.
Y2
) in Before proceeding, turn off the graphs
X Y3.
is an increasing exponential curve.
Y2
The calculator's
X,T,θ,n .
It is always a good idea to check
as the input variable).
may or may
Y2
(evaluated at a
Y1
Y1.
in the
ASK
2ND GRAPH (TABLE)
column.
X
X.
and are the same function.
Y2 Y3
as the input variable.
X
(evaluated at a
Y1
57