Estimate f ' (2.5) given the following table of values:
Answer
For each problem, we rearrange the information given into a more familiar table, then calculate the slopes.
As h approaches 0 from the right we find the slopes 6 and 10. As h approaches 0 from the left we find the slopes 5 and 9. We estimate that f ' (2.5) is in between 9 and 10.
Example 2
Estimate g ' (4) given the following table of values:
Answer
We estimate that g ' (4) is in between 0.2 and 0.4. Notice that we used g instead of f for the function name; this changes the labels on the tables but nothing else.
Example 3
Estimate f ' (2) given the following table of values:
Answer
It looks like f ' (2) is between 1 and 2. We had more values of a + h to the left of 2 than we did to the right of 2, but that's not going to change the way we do things.
