00:01
With a function f, we want to find first f of a.
00:07
You find f of a by plugging a in for x, so it's 1 over a plus 1.
00:13
And then f of a plus h is found by plugging a plus h in for x.
00:19
So it's 1 over a plus h plus 1, and there's nothing to simplify.
00:22
That is it.
00:24
Now, the difference quotient, f of a plus h minus f of a, all over h, we've already found each of these.
00:33
So it would be 1 over a plus h plus 1, minus 1 over a plus 1 all over h.
00:42
Now some algebraic simplifying here.
00:47
Dividing by h is the same thing as multiplying by 1 over h.
00:52
And then we need a common denominator for our numerator.
01:00
So in order to get that, let's catch up here.
01:06
We'll say it's 1 over h times the first term will need the denominator a plus 1.
01:15
So it would be a plus 1 in the numerator over a plus h plus 1.
01:20
And the second numerator will need the denominator of the first fraction, which would be minus a plus h plus 1...