[BlindMath] Average Rate of Change problem

[David Moore]

In my senior year of high school, our teacher chose a precalc textbook that had two great chapters on limits.
I knew a lot about limits, when I took calculus in college, because our high school teacher chose this book. He told us he chose this book because he wanted us to know limits before we went to college and took calculus.
David Moore

                                                                                                                                                                                                                Sent from Mail for Windows 10

From: Joseph C. Lininger via BlindMath
Sent: Sunday, August 19, 2018 10:56 PM
To: Blind Math list for those interested in mathematics
Cc: Joseph C. Lininger
Subject: Re: [BlindMath] Average Rate of Change problem

Sabra,
If some precalc classes teach limits, the practice definitely is not 
universal. I never studied limits in precalc, I didn't see them when I 
lead supplimental instruction sessions for a precalc course at my 
college, and I never found them in any of the precalc books I've looked 
through on the topic. That doesn't mean there isn't a class out there 
that includes limits though. It is entirely possible someone out there 
is teaching a precalc class with limits in it. After all, if you teach 
asymptotes, which you definitely do see in both algebra and precalculus, 
you are getting very close to teaching limits.

As for your conjecture that maybe they want the limit, I can definitely 
say that at least for this problem they do not want that. After all, 
they give an interval and they specifically ask for an "average rate of 
change." What they're looking for is for the person to plug the upper 
and lower bounds into the F function, then use the average rate of 
change formula.

--
Joe

On 8/19/2018 22:29, Sabra Ewing wrote:
> Hello. Limits actually are part of pre-calculus. That could be what they want is for you to get the limit of the function.
>
> Sabra Ewing
>
>> On Aug 19, 2018, at 8:16 PM, Joseph C. Lininger via BlindMath <blindmath at nfbnet.org> wrote:
>>
>> Susan,
>> Warning to others, I'm going into a bit of calculus in this message, which is beyond the original scope of the question asked by the original poster. I need to in order to answer Susan's question.
>>
>> You understand correctly regarding average rate of change being used as a tool for preparing the student to understand derivative. In fact, all you have to do to turn that average into a derivative is to take the limit of the average as (x_2 - x_1) goes to 0. Its normally rewritten a bit to look like this.
>>
>> (f(x + h) - f(x)) / (h)
>>
>> Now, take the limit as h goes to 0 and you'll get the derivative of f(x). So the average rate of change expression is extremely close to the expression for finding a derivative.
>>
>> --
>> Joe
>>
>>> On 8/19/2018 18:42, Susan Jolly via BlindMath wrote:
>>> Hi Bill,
>>>
>>> You are correct that except for a linear function this formula will
>>> typically give different results for different intervals. But my
>>> understanding is that this formula represents a standard definition which is
>>> useful background information intended to help a student appreciate the
>>> definition of a derivative once they get to calculus.
>>>
>>> Susan J.
>>>
>>>
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