Difference Quotients

A difference quotient is typically thought of to be just an equation, but it is simply a more complex variation of the slope formula.

The equation for a difference quotient is: 

In class, we derived this formula.  The picture below shows a slight variation of how this formula may be derived.  The difference quotient can be used to find the slope of individual portions of graphs of polynomial or exponential functions.  As you can see, if you use the basic slope formula given the values of x and y (x,f(x)) and (x+h,f(x+h)), the simplified result is the difference quotient.

Caution:When solving difference quotient problems, never try to set anything equal to zero; it is only an expression.

Here are a few example problems of how to solve difference quotient problems given a function f(x):

And with a polynomial function:

Have a great day!!!!! Julia Wilkins