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lecture14

# lecture14 - y = 1 x 2 ± 2 at ± 2 1 2 ² ex If h x = f x g...

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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 )] =

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Proof:
ex. If h ( x ) = ( x 2 + 3)( p x ± 2 x 2 ), ±nd h 0 (1).

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The Quotient Rule: If f and g are both di±erentiable, then d dx ± f ( x ) g ( x ) ² =
ex. If f ( x ) = 3 x 2 ± 3 e x , ±nd f 0 ( x ).

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ex. Find f 0 ( x ) if f ( x ) = 4 x x 2 + 1 : Find the equation of all horizontal tangent lines to f ( x ).
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.

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ex. Find the equation of the normal line to

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Unformatted text preview: y = 1 x 2 ± 2 at ± 2 ; 1 2 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)?...
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