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The Difference Quotient Review

Here's one that's messy to clean up:

Givenf( x ) = 2 / ( x + 1 )

 

So,f( blob ) = 2 / ( blob ) + 1 --> f( x + h ) = 2 / ( ( x + h ) + 1 )
 

 

( f( x + h ) - f( x ) ) / h = ( ( 2 / ( x + h ) + 1 ) - 2 / x + 1 ) / h * ( x + h + 1 )( x + 1 ) / ( x + h + 1 )( x + 1 ) ... ditch the compound fraction! ... = ( 2( x + 1 ) - 2( x + h + 1 ) ) / ( h( x + h + 1 )( x + 1 ) ) = ( 2x + 2 - 2x - 2h - 2 ) / ( h( x + h + 1 )( x + 1 ) = -2h / ( h( x + h + 1 )( x + 1 ) ) = -2 / ( x + h + 1 )( x + 1 )

 

YOUR TURN:

Givenf( x ) = 5 / x

 

Find( f( x + h ) - f( x ) ) / h

 

ADVICE:  Memorize this thing now!

( f( x + h ) - f( x ) ) / h