[BlindMath] Average Rate of Change problem

[Joseph C. Lininger]

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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