This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
This note was uploaded on 02/29/2012 for the course MATH 119 taught by Professor Maanomran during the Fall '09 term at Indiana UniversityPurdue University Fort Wayne.
 Fall '09
 MaanOmran
 Derivative, Rate Of Change, Slope

Click to edit the document details