[BlindMath] Average Rate of Change pr
Joseph C. Lininger
devnull-blindmath at pcdesk.net
Mon Aug 20 02:08:00 UTC 2018
Yes, you can. Average rate of change is just that, an average. If you
want the actual rate of change you need the derivative from calculus. If
you want the average over a given itnerval, however, the average rate of
change formula can be used no matter what kind of function it is. That's
actually the reason they're doing this in precalc. It gets very close to
computing the derivative. (Remember the general form of a derivative and
you'll see what I mean.) IN this case, it's a "plug and chug" sort of
problem, but it is always so when discussing average rate of change. The
average is defined only over a given interval of the function in question.
--
Joe
On 8/19/2018 18:13, 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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>
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