lecture14

# lecture14 - ex At what point(s do the tangent lines to y =...

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Lecture 14: Product and Quotient Rules (Chapter 3, Section 14) 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 diﬁerentiable, then d dx [ f ( x ) g ( x )] =

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2 Proof:
3 ex. If h ( x ) = ( x 2 +3) ± p x ¡ 2 x , use the Product Rule to ﬂnd the slope of the tangent line to h ( x ) at x = 1.

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4 ex. Find each point at which f ( x ) = xe x has a horizontal tangent line. Then ﬂnd f 00 ( x ).
5 The Quotient Rule: If f and g are both diﬁerentiable, then d dx ± f ( x ) g ( x ) =

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6 ex. Find f 0 ( x ) if f ( x ) = 4 x x 2 + 1 : Find the equation of all horizontal tangent lines of the graph of f ( x ).
7 ex. Find the equation of the normal line to y = 1 x 2 ¡ 2 at x = 2.

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8 ex. If f ( x ) = ( x ¡ 2) 2 x , ﬂnd f 0 ( x ) : Find each x -value at which the tangent line to f ( x ) is parallel to the line 35 x + y = 4.
9 ex. If h ( x ) = x 2 ¡ 3 xf ( x ) , f ( ¡ 2) = 3 ; and f 0 ( ¡ 2) = 1 2 , ﬂnd h 0 ( ¡ 2).

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Unformatted text preview: ex. At what point(s) do the tangent lines to y = x 3 + x 2 x pass through the point (2 ; Â¡ 3)? 11 Try These! 1) Suppose f and g are functions so that f (2) = 3, f (2) = Â¡ 1, g (2) = 5 and g (2) = 1 3 . a) Find h (2) if h ( x ) = f ( x ) g ( x ) . Write the equation of the tangent line to h ( x ) at x = 2. b) Find H (2) if H ( x ) = f ( x ) Â¢ (2 + 3 g ( x )). 2) If f ( x ) = ( x 2 + 2 x + 3) 2 , ï¬‚nd f ( x ) using the Product Rule. Write your answer in simplest form. 3) Find each x-value at which f ( x ) = 3 Â¡ x 2 e x has a horizontal tangent line....
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lecture14 - ex At what point(s do the tangent lines to y =...

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