Thomas' Calculus, Media Upgrade (11th Edition)

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Math 2253 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 b) x x x f cos 4 2 ) ( + = , ] , 0 [ π 2. Find the extreme values of the function and where they occur. a) 4 2 ) ( 3 + - = x x x f b) 1 ) ( 2 + = x x x f 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 b) ] 3 , 1 [ , 1 ) ( - = x x f 4. Find all possible functions with the following derivative. a) x y 2 = b) 1 2 - = x y c) 1 2 3 2 - + = x x y d) 2 1 sin 2 x x x y + + = 5. Use the Second Derivative Test to find any local extrema of the function a) ) 1 ( 2 ) ( 2 2 x x x f - = b) 4 2 4 ) ( x x x f - = 6. Find the length and width of a rectangle that has the perimeter 100 meters and the maximum area. 7. What is the largest possible area for a right triangle whose hypotenuse is 5 inches long? 8. An open-top box is to be made by cutting small congruent squares from the corners of a 6-in.-by-6-in. sheet of tin and bending up the sides. How large should the squares cut from the corners be to make the box hold as much as possible?
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