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.
Estimate g ' (4) given the following table of values:
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.
Estimate f ' (2) given the following table of values:
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.
Make it rain.
The who, what, where, when, and why of all your favorite quotes.
Go behind the scenes on all your favorite films.