hw10 - padilla (tp5647) Homework10 Fouli (58320) This...

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Unformatted text preview: padilla (tp5647) Homework10 Fouli (58320) This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Let f be the function defined by f (x) = x - cos 2x, - x . 1 Determine all interval(s) on which f is decreasing. 1. [-, - 5 ], [ 7 , ] 12 12 2. [- , - 12 ], [ , 6 6 11 12 ] 11 12 ] 11 12 ] 11 12 ] Determine the increasing and decreasing properties of the function f (x) = (x - 5) (x + 2) on its natural domain. 3 3 1. inc: (-, - 5 ] [5, ), dec: [- 5 , 5] 4 5 1 5 3. [- 5 , - ], [ , 12 6 6 4. [- 5 , - 12 ], [ 7 , 12 12 2. inc: (-, -2] [5, ), dec: [-2, 5] 3 3. inc: [-2, - 5 ], dec: [- 3 , ) 5 3 3 4. inc: [- 5 , 5], dec: [-2, - 5 ] [5, ) 3 3 5. inc: [-2, - 5 ] [5, ), dec: [- 5 , 5] 5. [- 5 , - ], [ 3 , 12 8 8 004 (part 1 of 2) 10.0 points Let f be the function defined by 1 f (x) = x 4 + x2 - x4 . 5 (i) Determine the derivative of f . 1. f (x) = (1 + x2 )(5 + x2 ) 2. f (x) = (1 + x2 )(4 - x2 ) 3. f (x) = (1 - x2 )(5 + x2 ) 4. f (x) = (1 - x2 )(4 - x2 ) 5. f (x) = (1 + x2 )(5 - x2 ) 6. f (x) = (1 - x2 )(4 + x2 ) 005 (part 2 of 2) 10.0 points (ii) Find the interval(s) on which f is increasing. 002 10.0 points Find all values of x at which the graph of y = x2 + 4 sin x changes concavity on (-/2, /2). 1. x = 6 3 3. x = - , 6 6 4. x = - , 3 3 5. x = 3 2. x = - 6. there are no values of x 7. x = - 6 003 10.0 points 1. [-2, 2 ] padilla (tp5647) Homework10 Fouli (58320) 2. (-, - 5 ], [ 5, ) 3. ( - , -1 ], [ 1, ) 4. (-, -2 ], [ 2, ) 5. [ - 1, 1 ] 6. [- 5, 5 ] 006 10.0 points 4. local maximum at x = -2 5. local maximum at x = 2 008 10.0 points 2 Let f be the function defined by f (x) = 1 + x2/3 . Consider the following properties: A. has local maximum at x = 0 Which does f have? B. concave up on (-, 0) (0, ) Find all points x0 at which 4+x f (x) = (x + 2)2 has a local minimum. 1. x0 = -2 2. x0 = -6 3. x0 = -4 , -2 4. x0 = 6 5. no such x0 exist 6. x0 = 6 , -6 7. x0 = -4 007 10.0 points The derivative of a function f is given for all x by f (x) = (3x2 + 6x - 24) 1 + g(x)2 where g is some unspecified function. At which point(s) will f have a local maximum? 1. local maximum at x = -4, 2 2. local maximum at x = 4 3. local maximum at x = -4 1. neither of them 2. A only 3. B only 4. both of them 009 10.0 points If f is a continuous function on (-5, 3) whose graph is 4 2 -4 -2 2 which of the following properties are satisfied? A. B. C. f (x) > 0 on (-2, 1), f has exactly 3 local extrema, f has exactly 4 critical points. padilla (tp5647) Homework10 Fouli (58320) 1. none of them 2. A and C only 3. B only 4. A only 5. B and C only 6. all of them 7. A and B only 8. C only 010 10.0 points 8 7 6 3. 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 3 6 4 2 -6 -4 -2 -2 -4 -6 1234567 2 4 6 Which of the following is the graph of f (x) = 8 7 6 1. 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 7 6 2. 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 x-2 ? x+1 6 4 2 -6 -4 -2 -2 -4 -6 6 4 2 -6 -4 -2 -2 -4 -6 2 4 6 2 4 6 -8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 -8-7-6-5-4-3-2-10 7 6 4. 6 5 4 4 3 2 2 1 0 -1 -2 -6 -4 -2 -2 -3 -4 -4 -5 -6 -6 -7 -8 8 -8-7-6-5-4-3-2-10 7 6 5. 6 5 4 4 3 2 2 1 0 -1 -2 -6 -4 -2 -2 -3 -4 -4 -5 -6 -6 -7 -8 -8-7-6-5-4-3-2-10 7 6 6. 6 5 4 4 3 2 2 1 0 -1 -2 -6 -4 -2 -2 -3 -4 -4 -5 -6 -6 -7 -8 -8-7-6-5-4-3-2-10 2 4 6 1234567 2 4 6 1234567 2 4 6 1234567 011 10.0 points Which of the following statements about the absolute maximum and absolute mini- -8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 padilla (tp5647) Homework10 Fouli (58320) mum values of f (x) = x3 - 5x2 - 7x - 1 x+1 1. 4 on the interval [0, ) are correct? 1. abs. max. = 15, abs. min. = -10 2. abs. max. = 6, no abs. min. 3. no abs. max., abs. min. = -1 4. no abs. max., abs. min. = -10 5. abs. max. = 15, no abs. min. 012 Find the value of x 2. 10.0 points lim f (x) 3. when 6x2 - 1 3x3 + 2x + 4 f (x) < . 2x2 x3 1. limit = 2. not enough information given 3 3. limit = 2 4. limit = 3 5. limit = - 6. limit = 6 013 10.0 points 5. 4. The following graphs have similar horizontal asymptotes, as indicated by the dashed lines, and each graph passes through the origin. Decide which one of them is the graph of x . f (x) = - 2+1 x padilla (tp5647) Homework10 Fouli (58320) 6. 5. limit = 3 7 016 Determine if lim 3x3 - 5x 2x3 + 5x2 + 2 10.0 points 5 014 10.0 points x Find all asymptotes of the graph of y = 4x2 - x - 3 . 4x2 - 7x + 3 exists, and if it does, find its value. 1. limit does not exist 2. limit = 5 2 3 1. vert: x = , horiz: y = -1 4 3 2. vert: x = , horiz: y = 1 4 3. vert: x = -1, horiz: y = -1 3 4. vert: x = - , horiz: y = 1 4 5. vert: x = 1, horiz: y = 1 015 10.0 points 3. limit = 1 4. limit = 2 5. limit = 3 6. limit = 3 2 017 10.0 points A certain function f is known to have the properties x - Which of the following is the graph of f (x) = x3 ? x2 - 9 lim f (x) = 5, x lim f (x) = 7 . Determine if x 0- lim 3 + 2x 1 2+f x exists, and if it does, compute its value. 1. limit does not exist 2. limit = 3. limit = 1 3 2 9 5 4. limit = 7 11 10 9 1. 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 8 4 -8 -4 -4 -8 -12 -10 -11 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 11 4 8 padilla (tp5647) Homework10 Fouli (58320) 11 10 9 2. 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 6 8 4 -8 -4 -4 -8 4 8 -11 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 11 11 -12 -10 10 9 3. 8 8 7 6 5 4 4 3 2 1 0 -1 -2 -8 -4 4 8 -3 -4 -4 -5 -6 -7 -8 -8 -9 -10 -11 -12 12 -12 -10 11 11 -11 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 10 9 4. 8 8 7 6 5 4 4 3 2 1 0 -1 -2 -8 -4 4 8 -3 -4 -4 -5 -6 -7 -8 -8 -9 -10 -11 -12 -12 -10 -11 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 11 ...
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