Average rate of change

1. Jan 23, 2010

chops369

1. The problem statement, all variables and given/known data
I have just started my first ever calculus course, and I'm having a little trouble with a simple rate of change problem.

It says: Find the average rate of change of the given function between the following pairs of x-values.

The given function is f(x) = x2+ x
The given values are x=1 and x=3

2. Relevant equations
Aren't I supposed to make use of the equation f(x+h) - f(x) / h ?
I don't really understand what h is supposed to be.

3. The attempt at a solution
I checked what the answer should be and it shows: f(3) - f(1) / 2 = 12-2 / 5 = 5

I understand the algebra and how it equates to the answer 5, but where did the two in the denominator come from? I feel like I'm not understanding some fundamental aspect of this problem and rates of change in general.

2. Jan 23, 2010

Bohrok

To find the average rate of change between point (a, f(a)) and (b, f(b)), you use
(f(b) - f(a))/(b - a). This is basically the same as finding the slope between two points m = (y2 - y1)/(x2 - x1), which you should be familiar with.

There's really no point in using the difference quotient (f(x+h) - f(x))/h, which is an expression, not an equation, for this problem.

3. Jan 23, 2010

chops369

Oh, ok. That makes sense. For some reason the equation you mentioned I should use isn't shown in my book.

4. Jan 24, 2010

Staff: Mentor

The expression Bohrok mentioned, namely (f(b) - f(a))/(b - a). An equation has an = sign between two expressions.

5. Jan 24, 2010

HallsofIvy

And, taking h= b-a, the difference between the two points, b= a+ h so the formula you cite, (f(a+h)- f(a))/(h)f(b)- f(a)/(b- a), becomes (f(b)- f(a))/(b- a).