[BlindMath] Average Rate of Change pr

[Doug and Molly Miron]

Hello Bill,


Since rate of change of the function is its derivative, the average rate 
of change over an interval is the original function evaluated at the end 
points, dividedc by the interval length, as I and several others have 
stated.


Regards,
Doug Miron
On 8/19/2018 5:13 PM, Bill Dengler via BlindMath wrote:
> Yes, but remember the function is not linear. Can you still calculate average rate of change this way, even though the instantaneous rates of change differ over the interval? This is why I suggested integration and dividing by the length of the interval.
>
> Bill
>
>> On 19 Aug 2018, at 21:37, Susan Jolly via BlindMath <blindmath at nfbnet.org> 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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