00:01
They want us to, let's see, show that.
00:09
No, they want us to find the value of the limit.
00:11
They want us to find the value of the limit as h approaches zero of this one's interesting.
00:17
F of a plus h minus 2 f of a plus f of a minus h all over h squared.
00:29
Oh, interesting.
00:31
Here he is.
00:35
We can try manipulating that in a bit.
00:37
They also tell us that a is a real number, and the second derivative exists.
00:44
Let's see.
00:46
I hope you remember your formula for derivatives.
00:50
Let's talk about the derivative as a limit, but the second derivative is a limit.
00:54
So what function are we taking the limit of? the limit as age approaches zero of our first derivative.
01:01
Let's see, f prime of a plus h minus f of a over h.
01:07
That one's perfectly acceptable.
01:11
However, we could also, let's see, have row in it as the limit.
01:20
As h approach is 0, f prime of a minus h.
01:26
And it's f of a over h.
01:30
Okay.
01:34
F prime, neat.
01:37
Well, what is the derivative? f prime of a plus h? well, that one's just the limit...