[BlindMath] Average Rate of Change pr

[Doug and Molly Miron]

Good day Susan,


I think all of us that previously responded to Elise's query agree that 
the function in question is f(x)=x^2 - x-+1.  We took somewhat different 
approaches to how to find the average rate of change, but we mostly 
agreed on the result.  Notation when writing in ASCII is an issue, and 
some of us have too much experience to keep it down to a novice level, 
unfortunately.  I would like to hear from Elise whether any of this has 
been useful to her.


Regards,

Doug Miron


On 8/19/2018 4:37 PM, Susan Jolly via BlindMath wrote:
> These answers got me confused and I've studied a lot of calculus.  But 
> remember this is pre-calculus.
>
> First the average rate of change of a function over a certain interval 
> is not the same as the average of the function itself over that same 
> interval. Finding the average rate of change just requires a simple 
> formula whereas find the average of the function is something more 
> complex one will learn about in calculus.
>
> Remember that the notation f(x) means a general formula for 
> calculating y if you know x whereas f(x_1) or f(x_2) means the value 
> of y at the specific points x_1 or x_2.
>
> The formula for the average rate of change defined to be
> a = [f(x_2) - f(x_1)]/(x_2 - x_1)
>
> It would be nice to understand why this formula is correct but first 
> you should memorize the formula and be able to use it.
>
> In this  case the function is f(x) = x^2 - x + 4.
>
> The value of this function when x = 2 is 6.
> The value of this function when x = 6 is 34.
> (Being able to plug numbers  into formulas and find the result is one 
> of the things you are supposed to be comfortable with.)
>
> so a = (34 - 6) / (6 - 2 ) = 28/4 = 7.
>
> HTH,
> Susan Jolly
>
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