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.

h10.10.010.0010.0001
Ave. Rate of Change of C59.79959.799959.7999959.79999959.7999999

(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,

 


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