[BlindMath] Average Rate of Change problem

[Bill Dengler]

When you’re looking for the average (arithmetic mean) of a set of data, you add up the values and divide by the number of values you have. For example, the mean of {5, 10, 15, 20, 25}=(5+10+15+20+25)/5=75 and 75/5=15, so the mean over your set of data is 15.
Another way of saying this: the average of a set of data is the total sum of the set divided by the number of values. By extension, the average rate of change is the total change of the function over the given interval, divided by the length of the interval.
Differentiation gives the instantaneous rate of change at any point, while integration gives the total change over a range of values, which is what we want.
Your function didn’t come out the best, but I’m assuming it’s x^2-x+4.
So, we need to do:
\int_{2}^{4}x^2-x+4dx
The power rule for integrals is x^n=x^(n+1)/(n+1), so:
\int x^2-x+4dx=(x^3/3)-(x^2/2)+4x+c
\int_{2}^{4}x^2-x+4dx=50/3
(50/3)-(4-2)=25/3

Bill

> On 18 Aug 2018, at 11:54, Elise Berkley via BlindMath <blindmath at nfbnet.org> 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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