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The Difference Quotient

Let's start working this thing out.  Here's the original function:

f( x ) = x + 2

Here are the pieces:

1 ) f( x + h ) :

Do the blob thang! f( blob ) = ( blob ) + 2

So f( x + h ) = ( x + h ) + 2 ... = x + h + 2 ... we don't need the ( ) here

2 ) -f( x ) :

This is just subtracting the original function

-f( x + 2 ) ... ( ) is important!

3 ) Just stick an h under everything and clean up that bad boy!

Here we go!

f( x + h ) - f( x ) / h = [ x + h + 2 ] - ( x + 2 ) / h ... the [ x + h + 2 ] is f( x + h ) ... the ( x + 2 ) is f( x ) ... clean it up! ... = x + h + 2 - x - 2 / h = h / h = 1

Continued on the next page