Math CentralQuandaries & Queries


Question from Tom, a student:

For the function x/3x-1 find the average rate of change between the interval x=1 and x=5?

Hi Tom,

The average of a function g(x) from a to b is

average of a function

Let f(x) = x/(3x - 1) then the rate of change of f(x) is given by f '(x) thus you want the average of f '(x) from 1 to 5.

Look carefully at what you have to do. This problem is much easier than it seems.


Tom wrote back

I get the answer: (5/14) - (1/2) / (4) which = -1/28 but this is wrong.
I thought I was finding the slope of the secant line between x=1 x=5 for the function, hence the average rate of change.
Can you explain what i'm doing wrong and give me a correct answer? Thankyou

Hi again Tom,

I got the same numerical answer as you, -1/128 by using the technique in my earlier response. Can you tell me why you say "this is wrong"? Do you know what the "correct answer" is supposed to be?


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