E. ESTIMATING A DERIVATIVE
E1. Numerically.
EXAMPLE 22
The table shown gives the temperatures of a polar bear on a very cold arctic day (t = minutes; T
= degrees Fahrenheit):
t 0 1 2 3 4 5 6 7 8
T 98 94.95 93.06 91.90 91.17 90.73 90.45 90.28 90.17
Our task is to estimate the derivative of T numerically at various times. A possible graph of T(t)
is sketched in Figure N3–3, but we shall use only the data from the table.
FIGURE N3–3
Using the difference quotient with h equal to 1, we see that
Also,
and so on.
The following table shows the approximate values of T ′(t) obtained from the difference
quotients above:
t 0 1 2 3 4 5 6 7
