HW_3_2_mod

HW_3_2_mod - at the point P ( 1 , 0.6 ). y = 7) Find an...

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Student Name: Sections 3.2 (Due: either Tuesday, 09/25 in class or Wednesday, 09/26 in my mailbox) Description : This homework will help you compute derivatives using the Product and Quotient Rules. Show all work to get full credit. 1) Find the derivative of y = ( x 2 + 5 )( x 3 + 4 ) in two ways. (a) Using the Product Rule. (Note: Do not simplify after applying the rule.) y ' = (b) By performing the multiplication first. (Note: Simplify completely after finding the derivative.) y ' = (c) Do your answers agree? yes no 2) Find the derivative of the function below in two ways. (a) By using the Quotient Rule. F '( x ) = (b) By simplifying first. F '( x ) = (c) Show that your answers are equivalent. (d) Which method do you prefer? the Quotient Rule simplifying first 3) Differentiate. 4) Differentiate the following function.
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Student Name: 5) Differentiate 6) Find an equation of the tangent line to the given curve
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Unformatted text preview: at the point P ( 1 , 0.6 ). y = 7) Find an equation of the tangent line to the curve at the given point. (Assume the tangent line form to be f(x) = mx + b .) m = b = 8) Suppose that f ( 5 ) = -6 , f '( 5 ) = -4 , g ( 5 ) = 6 , and g '( 5 ) = 4 . Find the following values. (a) ( fg )'( 5 ) = (b) ( f / g )'( 5 ) = (c) ( g / f )'( 5 ) = 9) If h (2) = 3 and h '(2) = -3 , find the following. 10) Find equations of the tangent lines to the curve below that are parallel to the line x- 2 y = 2. 11) A manufacturer produces bolts of fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q = f ( p ). Then the total revenue earned with selling price p is R ( p ) = pf ( p ). Given f (16) = 8000 and f' (16) = -320, find R' (16). 2740 2880 2950 3020 2810...
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HW_3_2_mod - at the point P ( 1 , 0.6 ). y = 7) Find an...

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