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Unformatted text preview: Using the definition f ( x + h ) = 2( x + h ) + 3 = (2 x 2 h + 3 ) = 2 f ( x+h ) – f ( x ) h f ' ( x ) = lim h = (2 h ) h lim h = (2 x 2 h + 3 ) – (2 x + 3) h lim h f ( x + h ) – f ( x ) h f ' ( x ) = lim h Example: Use the definition of the derivative to obtain the following result: If f ( x ) = x 2 8 x + 9, then f ' ( x ) = 2 x 8 f ( x + h ) = ( x + h ) 2 8( x + h ) + 9 = ( x 2 + 2 xh + h 2 8 x8 h + 9 ) = 2 x  8 f ( x+h ) – f ( x ) h f ' ( x ) = lim h = (2 x + h 8) lim h = h (2 x + h 8) h lim h = (2 xh + h 2 8 h ) h lim h = ( x 2 + 2 xh + h 2 8 x 8 h + 9 ) – ( x 2 8 x + 9) h lim h f ( x + h ) – f ( x ) h f ' ( x ) = lim h Solution: Using the definition...
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 Fall '09
 MaanOmran
 Calculus, Derivative, Rate Of Change, Slope, lim

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