One procedure for using the TI-92 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  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^3-x)-e^(x^3-x) 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 2nd derivative.  selects y2(x), which should be the derivative. Then 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