00:01
So we have this function f of x, and what we're going to do first is we're going to find the value of f of x plus h.
00:07
So we're just going to plug in x plus h in for x.
00:11
We're going to have x plus h multiplied by 20 minus in parentheses x plus h.
00:19
And so we can simplify this a little bit.
00:22
I'm going to distribute this negative sign.
00:24
So we're going to have x plus h multiplied by 20 minus x minus h.
00:30
And now i can do this multiplication.
00:33
So we have 20 times x, which is going to be 20x, minus x squared, minus h times x, and then we're going to have plus 20 times h, minus x squared.
00:50
And if you're wondering how i found that, i just took the first term of our first factor, multiplied it through the second factor, and then took our second term and did the same thing.
01:01
So let's see if we can simplify this at all.
01:04
Do we have any terms that we can actually combine? we do, we have a negative hx and a negative x, which are equal to each other.
01:12
So this is going to be equal to 20x minus x squared minus 2hx plus 20h minus h squared.
01:23
And this is the value of our function f of x at x plus h.
01:30
The next thing we're going to do is we're going to take we found in part a and we're going to minus f of x from it...