| C'(100) | = | lim h→0 |
 h |
= | $59.80 per dumbbell set. |
The average rates of change of C over the intervals [100, 100+h] for h = 1, 0.1, 0.01, 0.001, and 0.0001 are given in the following table.
| h | 1 | 0.1 | 0.01 | 0.001 | 0.0001 |
| Ave. Rate of Change of C | 59.799 | 59.7999 | 59.79999 | 59.799999 | 59.7999999 |
(Enter 100+60*x-0.001*x^2 as the formula for C(x) and then enter the intervals a = 100, b = 100+h for smaller and smaller h -- for instance enter b = 100.001 for h = 0.001.)
This value is approaching 59.8 as h approaches zero. In other words,
| C'(100) | = | lim h→0 |
h |
= | $59.80 per dumbbell set. |
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