00:01
Here we're given a function, f of x, which is negative x squared minus 8x minus 13, and we want to evaluate the difference quotient for this function.
00:11
So the difference quotient is basically the first step in a derivative.
00:15
That's going to be f of x plus h minus f of x all over h.
00:21
So let's first find what is f of x plus h? that means let's replace x plus h in here.
00:28
So we have negative x plus h squared minus 8 times x plus h.
00:34
Minus 13.
00:37
So then let's simplify.
00:38
I'm going to distribute this negative and i'm going to foil the x plus h.
00:42
So i have negative x squared plus, oh, so minus because i'm distributing, h squared and minus 2xh.
00:51
And then i'll distribute the eight as well, minus eight x, sorry, minus x8x, x minus 8h, minus 13.
01:00
So that's f of x plus h.
01:02
Now we're going to subtract f of x...