[BlindMath] Fwd: Post Scriptum:Re: Average Rate of Change problem

[Doug and Molly Miron]

P. S. Elise

Before I got out of bed this morning, it occurred to me that I should 
have said, as some others have since, that (rate of change)=(slope of 
graph)=derivative=df/dx=f'(x).  This is for a function, like yours, 
which is continuous over an interval of a continuous variable, no breaks 
or jumps.  Averaging over a data set of discrete or sampled values is 
not quite the same thing, especially if the underlying process is not 
uniform, or evenly spaced on the independent variable.  I see that in 
several replies they have derived the same general result I did.  If one 
substitutes your expression into this result and do the algevbraic 
reduction, the result is avg. slope=x_2+x_1-1.  if x_2=x_1=x the result 
is 2x-1, the derivative of f(x) at x.----Doug

-------- Forwarded Message --------
Subject: 	Re: [BlindMath] Average Rate of Change problem
Date: 	Sat, 18 Aug 2018 09:49:24 -0500
From: 	Doug and Molly Miron <mndmrn at hbci.com>
To: 	FElise Berkley via BlindMath <blindmath at nfbnet.org>



Good day Elise,


The average of a function over an interval is the integral of the
function divided by the length of the interval.  In this case, the
function being averaged is the derivative of f(x), so the integral of
the derivative is the original vunction.  Therefore, the answer is
(f(x_2)-f(x_1))/(x_2-x_1).  I don't know the rules for your pre-calculus
course so I don't know if you're allowed to use this reasoning and have
to take some other, more complicated, approach such as a
finite-difference approximation.


Regards,

Doug Miron


On 8/18/2018 6:54 AM, Elise Berkley via BlindMath wrote:
> Hello, mathematicians.
> In my precalc class, we are studying "average rate of change." I am so
> stuck and I am asking for help with this problem.
> 	Find the average rate of change of f(x) = x2 – x + 4 from x_1  = 2 to x_2=6 .
> If anyone can help me with this, I would greatly appreciate it. Thanks!
> Elise Berkley
>
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