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Unformatted text preview: Math 137 Winter 2010 Assignment 7 Due Friday, March 12 All solutions must be clearly stated and fully justified. Use the format given on UWAce under Content, in the folder Assignments; it is the file Math 137 Assignment Templates . Text problems: Section 4.1: 14, 34, 50, 54, 60, 70 Section 4.2: 18, 20, 28 Section 4.4: 8, 10, 20, 30, 40, 44, 50, 56, 60, 70 Section 4.1: 14. a) Sketch the graph of a function that has two local maxima, one local minimum, and no absolute minimum. A typical example: b) Sketch the graph of a function that has three local minima, two local maxima, and seven critical numbers. A typical example: 34. Find the critical numbers of g(t) = 3t – 4 g ′ (t) = 3 if t > 4/3, – 3 if t < 4/3, so g ′ (t) is never 0, but it DNE at t = 4/3. So 4/3 is a critical number for g(t). 50. Find the absolute extremum values of f(x) = x 3 – 6x 2 + 9x + 2 on [– 2, 3]. 54. Find the absolute extremum values of 4 4 ) ( 2 2 + − = x x x f on [– 4, 4]. 60. Find the absolute extremum values of f(x) = x – ln x on [½, 2]. x x x x f 1 1 1 ) ( − = − = ′ . This is 0 when x = 1, and DNE when x = 0. However, 0 is not in the domain of f, nor in the interval under consideration, so we ignore 0. We check the critical number 1 as well as the endpoints ½ and 2: f(½) = ½ – ln(1/2) = ½ + ln 2 ≈ 1.193 f(1) = 1 – ln 1 = 1 Absolute minimum f(2) = 2 – ln 2 ≈ 1.307 Absolute maximum 70. An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle θ with the plane, then the magnitude of the...
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This note was uploaded on 04/13/2010 for the course MATH 137 taught by Professor Speziale during the Spring '08 term at Waterloo.
 Spring '08
 SPEZIALE
 Math

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