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The Difference Quotient Review

Here's another one:

 Givenf( x ) = 5x - 2x^2
 Do thef( x + h )part first!


    f( blob ) = 5( blob ) - 2( blob )^2

f( x + h ) = 5( x + h ) - 2( x + h )^2 = 5x + 5h - 2x^2 - 4xh - 2h^2
 

 

( f( x + h ) - f( x ) ) / h = ( ( 5x + 5h - 2x^2 - 4xh - 2h^2 )( 5x - 2x^2 ) ) / h = ( 5x + 5h - 2x^2 - 4xh - 2h^2 - 5x + 2x^2 ) / h ... the 5x's and the 2x^2's cancel out ... ( 5h - 4xh - 2h^2 ) / h = ( h( 5 - 4x - 2h ) ) / h = 5 - 4x - 2h

 

YOUR TURN:

Givenf( x ) = 3x^2 - 7x + 2

 

Find

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