Here is a worked example for a possibly different function:
R(t) = 7500 + 500t - 100t2
Use the following intervals for the average rates of change:
| h = 1: | | Interval: [1, 2] |
R(2) - R(1)
2 - 1 |
|
= 200 |
| h = 0.1: | | Interval: [1, 1.1] |
R(1.1) - R(1)
1.1 - 1 |
|
= 290 |
| h = 0.01: | | Interval: [1, 1.01] |
R(1.01) - R(1)
1.01 - 1 |
|
= 299 |
| h = 0.001: | | Interval: [1, 1.001] |
R(1.001) - R(1)
1.001 - 1 |
|
= 299.9 |
| h = 0.0001: | | Interval: [1, 1.0001] |
R(1.0001) - R(1)
1.0001 - 1 |
|
= 299.99 |
We therefore get the following table:
| h | 1 | 0.1 | 0.01 | 0.001 | 0.0001 |
| Ave. Rate of Change over [1, 1+h] | 200 | 290 | 299 | 299.9 | 299.99 |
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