Chap 3 Problems for Exam 2

Thomas' Calculus, Media Upgrade (11th Edition)

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Review Problems for Exam 2 (Covers chapter 3) 1. Find the derivative of the function by the limit process. a) 3 2 ) ( 2 + - = x x x f b) 1 ) ( + = x x f 2. Find an equation of the line that is tangent to the graph of ) 7 )( 8 ( ) ( 2 2 - - = x x x f at (3, 2). 3. Find the derivative of each of the following functions. (a) 6 3 2 ) ( 2 3 4 - + - + = x x x x x f (b) x x x f 4 ) ( 2 - = (c) 3 6 ) ( x x x f - = (d) 3 2 1 ) ( - - = x x x f (e) 4 2 ) 1 3 ( ) ( + - = x x x f 4. Find an equation of the line that is tangent to the graph of 2 2 3 ) ( x x x f + - = and parallel to the line 3 2 4 = + y x . 5. Find an equation of the line that is tangent to the graph of 2 3 ) ( x x f + = and perpendicular to the line 3 2 4 = + y x . 6. If 5 3 2 ) ( 2 + - + = x x x x f , find ) ( ) 4 ( x f . 7. A ball is thrown straight down from the top of a building. Its distance from the ground is given by the position function 2 16 22 220 ) ( t t t s - - = . Find its velocity and acceleration after 3 seconds. 8. Find the derivative of each of the following functions. (a) x x x f cos sin ) ( = (b) x x x x f cos sin 2 ) ( + = (c) x x x x f tan 2 ) ( 2 - = (d) x x y cot csc + = (e) 3 1 ) ( x x f - = (f) 6 2 1 ) 5 ( ) 5 2 ( ) ( x x x x f - - = - (g) ) 1 3 ( sin 2 ) ( 4 + = x x f
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