Here is one worked out for a similar, but not necessarily identical cost function. (If it is the same cost function as yours, then you are very lucky!)
Suppose your cost function was
Then 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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