Question

Rate of Change Formula and explanation, please?

Answer 1

Instantaneous or average rate of change?

Answer 2

Average.

Answer 3

An example that I could work out would probably help.

Answer 4

The average rate of change is simply the slope formula.... Example If a start my car at point A and drive 60 miles in 30 minutes what would be am average rate of change...

t(1) = 0 for starting time....d(1) = 0 for starting point.
t(2) = 30 for ending time d(2) = 60 for ending distance
\[Rate of change = ....\frac{ d1-d2 }{ t1-t2} = Rate of change per minute\]

Answer 5

Okay, that makes sense.

Answer 6

Instantaneous is somewhat different

Answer 7

So, when doing the average, can D be x or y?

Answer 8

I'm trying to find the average Rate of Change using x and y.

Answer 9

In his example, t would be x and d would be y. The variables are interchangable; you could use whatever variables you'd like.

Answer 10

Oh, okay.

Answer 11

And just to make sure, the D1 and D2, for example, have the 1 and 2 to show which variable or number is to be used, rather than saying D1 = 0 x 1. Is that correct?

Answer 12

Erm, wait...the slope formula was more like D2 - D1 over T2 - T1. Was the change accidental, or is that how it is for Average Rate of Change?

Answer 13

Average rate of change is the slope.

Answer 14

Yes, which would be D2 - D1, etc., rather than D1 - D2, right?

Answer 15

Average rate of change of f(x) in the interval \([x_1,x_2]\) is:

\(\Large \frac {f(x_2) - f(x_1)}{x_2-x_1} \)

Answer 16

D2-D1 is fine as long as it is T2-T1 as the denominator. It can be D1-D2 as long as it is T1-T2 as the denoinator

Answer 17

But wouldn't it give different answers if you did it as either way?

Answer 18

As in, if you went for:

wouldn't the results be different?

Answer 19

\(\Large \frac {a-b}{c - d} = \frac {b-a}{d-c} \)
Its is equivalent to multiplying both top and bottom by -1 which will not change the result.

Answer 20

Can I have an example used for Average Rate of Change? I feel like I'd understand it better that way.

Answer 21

Let f(x) = 3x^2
Find the average rate of change of f(x) between x = 1 and x = 4.

Will this example work for you? Or do you need something else?

Answer 22

Well, what I mean is, can we take the example, and go through the steps together? Through text like:
-3 - 3 over -2 - 2
-6 over -4
1.5

or through drawings?

Answer 23

f(x) = 3x^2
Find the average rate of change of f(x) between x = 1 and x = 4.
When x = 1, f(x) = 3*1^2 = 3
When x = 4, f(x) = 3*4^2 = 48

x f(x)
1 3
4 48

Average rate of change = (48 - 3) / (4 - 1) = 45 / 3 = 15
or
Average rate of change = (3 - 48) / (1 - 4) = -45 / -3 = 15

Answer 24

Oh, huh. I think I managed to use the Average Rate of Change for the original problem I had, and I see what you guys meant when you said it wouldn't change.

Answer 25

Okay, now that's a lot different, but maybe closer to what the problem is actually asking of me. I guess I'll show what the problem is so we can pinpoint what exactly I'm supposed to do.

Answer 26

Part C: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (3 points)

Answer 27

From the graph, when x = 2, what is the y value?
From the graph, when x = 5, what is the y value?

Answer 28

This was what I got:
1. Y2 - Y1 over X2 - X1.
2. 160 - 100 over 5 - 2.
3. 60 over 3.
4. 20. So, the Average Rate of Change is 20.
Y1 - Y2 over X1 - X2.
100 - 160 over 2 - 5.
-60 over -3.
20.

Answer 29

Correct.

Answer 30

Thank you, then! And I mean to all of you who responded. I have another question that I need help with, but I'm going to post it in a new question.

Answer 31

You are welcome.