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Coolmath Precalculus Review Calculus Preview
Lesson 24 - Tools - The Difference Quotient (page 4 of 4)
---- This Precalculus review (Calculus preview) lesson reviews the difference quotient and gives an intro to how it is used in Calculus.

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

Given

So,

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

YOUR TURN:

Given

Find

ADVICE: Memorize this thing now!

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

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