Thomas' Calculus, Media Upgrade (11th Edition)

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Review Problems for Exam 3 (Chapter 4) 1. Find the absolute maximum and minimum values of each function on the given interval. a) , 1 ) ( 2 - = x x f 2 1 - x (abs. Max = 3, abs. min = -1) b) x x x f cos 4 2 ) ( + = , ] , 0 [ π (abs. Max = π 2 , abs. min = 4) 2. Find the extreme values of the function and where they occur. a) 4 2 ) ( 3 + - = x x x f (local Max 9 6 4 4 + at , 3 2 - local min 9 6 4 4 - at 3 2 .) b) 1 ) ( 2 + = x x x f (local Max 2 1 at 1 ; local min 2 1 - at 1 - ) 3. Find the value or values of c that satisfy the equation ) ( ) ( ) ( c f a b a f b f = - - in the conclusion of the Mean Value Theorem for the following functions and intervals. a) ] 1 , 0 [ , 2 3 ) ( 2 + - = x x x f = 2 1 c b) ] 3 , 1 [ , 1 ) ( - = x x f = 2 3 c 4. Find all possible functions with the following derivative. a. x y 2 = ( 29 C x + 2 C is a constant. b. 1 2 - = x y ( 29 C x x + - 2 c. 1 2 3 2 - + = x x y ( 29 C x x x + - + 2 3 d. 2 1 sin 2 x x x y + + = + - - C x x x 1 cos 2 5. Use the Second Derivative Test to find any local extrema of the function a) ) 1 ( 2 ) ( 2 2 x x x f - = (Local min 0 at x=0. local Max 2 1 at 2
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