# Thread: Rate of change over an interval?

1. ## Rate of change over an interval?

I hope this is my last question of the day.

I found the derivative of a function, and now part 2 of the question is asking me to talk about the rate of change over a specific interval of time (ex. 10 minutes).

What is the question asking me to do?

Do I just sub in times into the derivative or is there another method?

2. Originally Posted by NAPA55
I hope this is my last question of the day.

I found the derivative of a function, and now part 2 of the question is asking me to talk about the rate of change over a specific interval of time (ex. 10 minutes).

What is the question asking me to do?

Do I just sub in times into the derivative or is there another method?
they want you to find the slope of the secant line.

you must compute: $\displaystyle \frac {f(t_2) - f(t_1)}{t_2 - t_1}$

where $\displaystyle t_1$ is the time you start measuring from, and $\displaystyle t_2$ is the time you stop

so, if it was from initial time to 10 minutes later, $\displaystyle t_1 = 0$ and $\displaystyle t_2 = 10$, for time in minutes

3. So that would suffice if it asked me to "comment on the rate of change"?

I'll do that then specific to my question (I was throwing out arbitrary numbers in my original post).

Thanks!

4. Originally Posted by NAPA55
So that would suffice if it asked me to "comment on the rate of change"?

I'll do that then specific to my question (I was throwing out arbitrary numbers in my original post).

Thanks!
no, that helps to find the rate of change. commenting on it is different. when commenting they expect you to tell them what it means. for instance, you can say something is increasing or decreasing over time, and why it makes sense for that to happen. stuff like that

5. The function increases rapidly, peaks, and gradually decreases. I determined that by graphing the function.

But the question never asked me to graph it.

So would I comment on the rate of change then by determining the rate of change over shorter intervals (ex. 1-4 minutes, 5 minutes, then 6-10 minutes) or something like that, and put into words how it's great, peaks, and then decreases?