00:01
Here, we're given the equation f of x, which is equal to 11 minus x squared.
00:07
And we want to find the slope of the tangent line using the definition of a derivative.
00:12
So what we need to find is the limit as h approaches and as h approaches zero of f of x plus h minus f of x over h.
00:22
So if i plug in f of x plus h, that's 11 minus x plus h squared.
00:29
And then i'm going to subtract my 11 minus x squared all over 8.
00:37
Now the first thing i'm going to point out is the 11s will just cancel away.
00:40
They don't matter.
00:42
But let's go ahead now distribute this x plus h squared.
00:46
So we have an x squared plus 2xh plus h squared.
00:52
That's that x plus h squared.
00:54
Let's remember that we have a negative here.
00:56
And then we're going to subtract a negative, so add x squared.
01:01
And we have over h.
01:03
So again, let's see what cancels away.
01:05
We have x squared minus x squared...