Calculating Average Rates (TI 85)

Goal: We want to calculate values of [f(x+h)-f(x)]/h for a variety of values of h and we want to be able to easily change the function f and then repeat the calculations.

General method: Set up the function, f, as y1. Use this function to successively calculate f(x+h) and f(x) and store the respective values in A and B. Then compute (A-B)/h.

Step by step example: Consider f(t)=x² ö x and the interval [2, 2.4]. Then we will want to calculate the average rate when x is 2 and h is 0.4. In this case, x+h is 2.4

• On the y(x)= screen, enter y1=x^2-x
  (Use GRAPH y(x)=)
• On the home screen, enter 2.4 x and then y1 A
• On the home screen, enter 2 x and then y1 B
• On the home screen, enter (A-B)/0.4 to display the desired result.

If you wish to repeat this for the same value of x but other values of h, note that B does not change. You will need to enter statements to change A and to recompute (A-B)/h. These can be combined on a single line:

• 2+h x : y1 A: (A-B)/h
  (where h is the required value)

Other values of h can then be used by recalling that line after its execution (use the ENTRY command to do this) and editing in a replacement for h in its two locations.

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