Evaluating a Difference Quotient

How to Answer

The goal in evaluating a difference quotient is to simplify, not solve for a variable.

This is the basic difference quotient:

Let's start with a simple function:

Now you substitute each f(blank) by plugging it into the function and substituting for x. Think of it as f(2). Plug that into the function and it becomes 2(2)=4. It is the same thing for f(x+h). Plug it in and it becomes 2(x+h)=2x+2h. So now let's evaluate the difference quotient.

Evaluate:,

First step it to plug in

 Now Distribute:Then combine like-terms:

 Simplify and divide out h

And your answer is 2 and

That's all there is to it. But lets look at one more problem.

Knowing When to Stop

Once again, the goal in evaluating a difference quotient is to simplify, not solve for a variable. Let's take the same problem, different function.

First Substitute:

 Use FOIL:  Simplify:

 Factor out h: Simplify

 And this is the answer:, 

DONE! Thats it. Don't do anything else. Don't set it equal to zero and try and solve for x and h.

Alright, I hope this helps. Feel free to ask questions if you have any. Thank you!