One procedure
for using the TI92 and calculus for graphing. Illustrated using problem
9 pg. 300 of Stewart's calculus text.

Store the function as y1(x)
From the Home screen ,
type
x 3 x
y1(x)
this stores the function as y1 for use in the Graph screen.
Check that the function was typed in correctly by checking the values
of the function at a few points where the calculations are easy.
Type y1(0) and verify
that the answer is 1. Check also that y1(1) and y1(1) are both 1.

Obtain the derivative expression,
y1(x),x)
This should cause the right display to read

Store the derivative expression in y2(x) by doing the following.
Move up and get the derivative expression by typing
This should cause 3*x^2*e^(x^3x)e^(x^3x) to appear on the entry
line.
Now use y2(x) to
store the expression as y2(x)

Obtain the second derivative,
y2(x),x)
and store it as y3(x), y3(x)

Now verify that the function and its derivatives are entered in the Y=
screen correctly.

We want a graph that contains all the "important" aspects of the curve.
This would include zeros, asymptotes, local extrema, and inflection points.
Most
of the time these can be obtained using the solve option.

clears
the entry line

y1(x)
0,x)gives the result of
false
which indicates there are no zeros. Inspection also shows that there are
no vertical or horizontal asymptotes.

y2(x)
0,x)solves for critical points
at

gives
numerical approximations to the critical points as .577350 and .577350..

y3(x)
0,x)solves for possible
inflection points at .146025 and –1.088703.

The minimum interval containing all these points is [1.088703, .577350].
We would normally want an interval that is larger. Suppose we begin with
[2,2] for the x bounds.

There are a number of ways to get good bounds for the y values.
One way might be to look at the functional values for all the "important"
x
values.
A way that is probably less time consuming is to begin with a standard
interval [10,10], look at the graphs, and adjust. A final suggestion is
to change the style on the derivative and 2^{nd} derivative.
selects y2(x), which should be the derivative. Then
2 should change the style
to dots. Follow a similar procedure to change the style of y3(x).

Set the window by and
setting xmin= 2, xmax=2, ymin= 10, ymax=10.

Look at the graphs

The largest and smallest values (except for values near 2) occur on the
y3(x)=f"(x) function. Use the trace option to estimate a maximum value
of a little over 4 at about x= 1.4, and a minimum value of about 5.7
at about x= .7. Use the key
to exit the trace option.

Go back to the
and reset ymin= 6 and ymax= 5. Regraph the function.
Created by T. J. Sanders, tjs@usna.edu