<p>Said by austin: "this is how you would do it (and how they did it):
(21-24)/(15-9) = -3/6 = -1/2"</p>
<p>Why would you use 21 vs. a closer number like 22??</p>
<p>you are trying to find the 'average slope'
I was referring to the closest x-values.</p>
<p>^^ I still dont understand...
"0 20
3 31
6 28
9 24
12 22
15 21"</p>
<p>What made you choose the numbers that you did to find W'(12)?</p>
<p>you want to get a close approximation of the slope at 12.
so you would choose x values that are close to 12.
Now, I think you are wondering why we didn't use f(12) minus f(9)?
That's because you are finding the 'average' slope at 12.
consider the graph of 2x^2
x y
0 0
1 2
2 8
3 18
4 32</p>
<p>Now, to find average slope at x=2,you would use values that are close to 2. Suppose you used f(4) and f(0), that wouldn't give you a good approximation of the slope at 2.
Now, if you use f(1) and f(3) to find average slope at x=2, you will get a better appoximation. 2 is in the middle of 1 and 2.
if you used f(1) and f(2), you will get too low a slope.
if you used f(2) and f(3), you will get too high a slope.
Remember: slope changes very quickly.</p>
<p>most of the times, they will give you the intervals.</p>
<p>christalena2, do you see what I am saying?
It's kind of hard to explain.</p>
<p>YES! I get it!</p>
<p>thanks. Im a little slow...
Kind of like how a midpoint reimann sum is more accurate than a left or right?</p>