00:01
Number 30, i'd like us to evaluate the difference quotient of the given function, and to simplify our answer, where f of x equals x cube, and we need to find f of a plus h minus f of a over each.
00:18
So how we go about this is first we find f of a plus h.
00:22
So what we do is we're going to replace x with a plus h, so we get a plus h, cube.
00:31
Minus we replace a with x a cubed over h and so we need to expand a plus h cubed and so for me the easiest way to expand is to use pascal's triangle basically a one one one two one because you're adding these and one one plus two is three two plus one is three and one and this is the number sequence for anything cubed.
01:05
And so we can use that to expand this.
01:10
We get equals a cubed times h to the 0, which will just be one.
01:20
We're going to leave that there for now.
01:26
Plus 3a squared.
01:29
You're going to subtract one from a, add one to h, h to 1 plus 3.
01:36
Subtract 1 from a, add 1 to h, h squared, plus 1.
01:43
We can leave that out...