The Difference Quotient
You probably saw this semi-obnoxious thing in Algebra... And I know you saw it in Precalculus. Go back and look at the Slopes of Lines lesson again... This thing is just the slope of a line through the points ( x, f(x) ) and ( x + h, f(x + h) ). It's going to be used in the most important Calculus theorems, so you really need to get comfortable with it. I know right where students get messed up on these, so let's back up a bit and start with some basics. We'll build up from there.
You're probably fine with the easy stuff:
| Given |  |
* Remember that parentheses ( ) are REALLY important on these!
TRY IT:
| Same function: |  |
| find |  |
| find |  |
| find |  |
Ha ha... I made you write "booger." I'm so mature.
| Now do |  |
(This is important! Use those parentheses!) |