Expert: Paul Klarreich - 4/29/2009

Question
1. Find the average rate of change of f(x)=(1/x+1) on the interval [0,4]. Can u how how u did it?


2.Find the average rate of change of h(x)= 2sinx+1 on interval [0,(pi/2)].

And can u give an example of a function with an interval in which that function has an average rate of zero on that interval?

Answer
Questioner:   michelle
Country:  United States
Category:  Advanced Math
Private:  Yes << CHANGED.
 
Subject:  algebra+trig
Question:  1. Find the average rate of change of f(x)=(1/x+1) on the interval [0,4]. Can u how how u did it?


2.Find the average rate of change of h(x)= 2sinx+1 on interval [0,(pi/2)].

And can u give an example of a function with an interval in which that function has an average rate of zero on that interval?
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Hi, Michelle,

Your definition of Average Rate of Change for f(x) on [a,b] should say:
           f(b) - f(a)
A.R.o.C. = -------------
             b - a

Now just apply it to your two examples.  Just determine your a, and your b, and do the substitution.  Carefully, of course, and parenthesize when needed so you don't blow any signs.
.................
Now if the average rate of change is zero, what does that say about f(a) and f(b)?  That should make it easy.

If you get stuck, send me what you did and we'll take it from there.