lecture14 - y = 1 x 2 2 at 2 ; 1 2 . ex. If h ( x ) = f ( x...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 14: Product and Quotient Rules (Sec. 3.2) ex. Let f ( x ) = x 2 and g ( x ) = x + 1. What is d dx [ f ( x ) g ( x )]? The Product Rule: If f and g are both di±eren- tiable, then d dx [ f ( x ) g ( x )] =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Proof:
Background image of page 2
ex. If h ( x ) = ( x 2 + 3)( p x ± 2 x 2 ), ±nd h 0 (1).
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Quotient Rule: If f and g are both di±erentiable, then d dx ± f ( x ) g ( x ) ² =
Background image of page 4
ex. If f ( x ) = 3 x 2 ± 3 e x , ±nd f 0 ( x ).
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ex. Find f 0 ( x ) if f ( x ) = 4 x x 2 + 1 : Find the equation of all horizontal tangent lines to f ( x ).
Background image of page 6
ex. If f ( x ) = ( x ± 2) 2 x , ±nd f 0 ( x ) : Find each x -value at which the tangent line to f ( x ) is parallel to the line 35 x + y = 4.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ex. Find the equation of the normal line to
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y = 1 x 2 2 at 2 ; 1 2 . ex. If h ( x ) = f ( x ) g ( x ) , f (2) = 3, f (2) = 1, g (2) = 5 and g (2) = 1 3 , nd h (2). ex. If h ( x ) = x 2 3 xf ( x ) , f (2) = 3 ; and f (2) = 1 2 , nd h (2). Additional Example ex. At what point(s) do the tangent lines to y = x 3 + x 2 x pass through the point (2 ; 3)?...
View Full Document

This note was uploaded on 02/10/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

Page1 / 11

lecture14 - y = 1 x 2 2 at 2 ; 1 2 . ex. If h ( x ) = f ( x...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online