Math_137_Winter_2010_Solution_7

Math_137_Winter_2010_Solution_7 - Math 137 Winter 2010...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 UW-Ace 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...
View Full Document

This note was uploaded on 04/13/2010 for the course MATH 137 taught by Professor Speziale during the Spring '08 term at Waterloo.

Page1 / 7

Math_137_Winter_2010_Solution_7 - Math 137 Winter 2010...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online