[BlindMath] Average Rate of Change problem

Joseph C. Lininger devnull-blindmath at pcdesk.net
Sat Aug 18 19:48:08 UTC 2018

Average rate of change is actually a relatively simple problem. You 
compute it as follows.

The fraction with numerator f(x_2) - f(x_1) and denominator x_2 - x_1

IN this case, use 6 for x_2 and 2 for x_1. So do the following.

1. Compute f(6) and f(2).
2. Subtract the results from step 1.
3. Compute 6-2.
4. Divide the result from step 2 by the result from step 3 to get the 
average rate of change.

I'm going to give you just a little bit of background because it will 
help you later on in Calculous. What you're doing when you compute an 
average rate of change is computing average slope of the function at any 
point on the graph of that function. (Rate of change and slope are 
basically the same thing) Obviously, you know that for a linear function 
like "y = 2x + 3", the slope is constant. It doesn't matter where on the 
graph you look, the slope will be constant. 2 in this case. Well, 
non-linear functions (the one you gave is a quadratic for instance) also 
have slope. The difference is that the slope varies depending on the 
value of x and y, and hence where you are on the graph. Computing the 
average rate of change tells you what the average rate of change and 
hence the average slope is given a particular function and and two 
boundary points. Notice how the equation for rate of change resembles 
the standard "rize over run" equation for slope of a line.


On 8/18/2018 07:54, Elise Berkley via BlindMath 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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