00:03
So in this problem, we're given the function f of x equals 2x cubed plus x.
00:15
We're asked to determine f prime at a.
00:23
Okay.
00:24
Well, by definition, f prime at a is the limit as h goes to zero of f of a plus h minus f of a all over h.
00:50
Okay, so first of all, we've got to figure out f of a plus h.
00:59
Well, that's two times a plus h cubed plus a plus h.
01:10
And so that's two times a cubed plus three.
01:21
A squared h plus three a h squared plus one let's see a p h sorry and that's plus a plus a plus h and so this becomes well i have two a cubed and i have three a squared h and i have three a that's not three sorry sorry this would be, and this one.
02:03
This would be six, and that would be six, and then plus an a.
02:16
By the way, this is h cubed over here, plus an h plus an h cubed, wouldn't it? okay.
02:32
And let me just make this a little clear.
02:37
Sorry about that.
02:38
Let's just make this look clear.
02:40
That's two h cubed plus a.
02:44
Plus h.
02:47
Okay.
02:50
F at a is simply 2a cubed plus a in it.
02:59
Okay.
03:05
So that means that f at a plus h minus f at a our numerator up here, right, our numerator up here.
03:18
Well, let's see.
03:20
The two a cubes are going to cancel out...