00:01
For this problem, we're given function f of t is equal to 4 over t.
00:05
4t is equal to a and a plus each.
00:09
Now we have two questions to answer.
00:13
The first one is determine the net change between the given values of the variable.
00:21
So really what it means here is we're taking our function f and we're plugging in these different values of the variable, this being the first one and this being the second one, and we're finding the difference between the two.
00:40
So usually we plug in the second one first.
00:45
So i'm going to do f of a plus h, and then i'm going to subtract, since i'm finding the difference, i'm going to subtract f of a.
00:56
So let's see what this looks like.
00:58
Our function, f, is 4 over the variable.
01:03
So for each of these, i'm going to have 4 over something.
01:08
That something is going to be the input.
01:11
For the first one, the input was a plus h.
01:13
So i'm going to have 4 over a plus h.
01:17
The second one, the input was just a.
01:19
So i'm just going to have a in my denominator.
01:23
And here we go.
01:24
We have the net change.
01:26
Now, this could either be the answer itself, or we could maybe do subtraction and simplify a bit.
01:31
So i am going to go a little further with this.
01:34
We're trying to do a subtraction between two fractions.
01:38
And of course, we need a common denominator first.
01:41
So let's go ahead and find that.
01:43
I think our least common denominator would be if we took a and a plus h and we multiply them to each other.
01:51
So for the first fraction, i think i do need to multiply in that a, both to the top and to the bottom of the fraction.
01:59
And for the second fraction, i need to multiply in the a plus h, both to the top and to the bottom.
02:08
Now what i have here is that now i have my common denominator.
02:12
It's a times a plus h.
02:14
So i have that on the bottom.
02:21
And then now i just need to subtract the numerators...