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HW_2_7

# HW_2_7 - f a f t = t 4 8 t f a = 5 The limit represents the...

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Student Name: Sections 2.7 (Due: Tuesday, 09/18) Description : This homework will help you understand different ways to interpret the derivative. Show all work to get full credit. 1) Consider the curve y = x - x 4 . (a) Find the slope of the tangent line to the curve at the point (1, 0). (b) Find an equation of the tangent line in part (a). y = 2) Consider the following curve. y = 5 + 4 x 2 - 2 x 3 . (a) Find the slope of the tangent to the curve at the point where x = a . m = (b) Find the equation of the tangent line at the point ( 1 , 7 ). f ( x ) = (c) Find the equation of the tangent line at the point ( 2 , 5 ). g ( x ) = 3) If a rock is thrown upward on the planet Mars with a velocity of 14 m/s, its height (in meters) after t seconds is given by H = 14 t - 1.86 t 2 . (a) Find the velocity of the rock after one second. m/s (b) Find the velocity of the rock when t = a . m/s (c) When will the rock hit the surface? t = seconds (d) With what velocity will the rock hit the surface? m/s 4) Find

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Unformatted text preview: f '( a ). f ( t ) = t 4- 8 t f '( a ) = 5) The limit represents the derivative of some function f at some number a . Select an appropriate f ( x ) and a . f ( x ) = x 9- x , a = 1 f ( x ) = x 9 + x , a = 0 f ( x ) = x 9 , a = 1 f ( x ) = x 10 , a = 0 f ( x ) = x 8 , a = 2 6) This limit represents the derivative of some function f at some number a . Select an appropriate f and a . f ( x ) = x 1/4 , a = 16 f ( x ) = x 1/4 , a = 2 f ( x ) = √ x , a = 16 Student Name: f ( x ) = √ x , a = 4 f ( x ) = x 4 , a = 2 7) The limit represents the derivative of some function f at some number a . Select an appropriate f ( x ) and a . f ( x ) = 3 x , a = 4 f ( x ) = 4 x , a = 81 f ( x ) = 4 x , a = 3 f ( x ) = x 3 , a = 4 f ( x ) = 3 x , a = 81 8) Determine whether f '(0) exists. yes no 9) Determine whether or not f '(0) exists. If it exists, give its value. If it does not exist, enter NONE....
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HW_2_7 - f a f t = t 4 8 t f a = 5 The limit represents the...

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