HW10 - myers (nmm698) – HW10 – Hamrick – (54868) This...

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Unformatted text preview: myers (nmm698) – HW10 – Hamrick – (54868) This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points 2. f (1) < f ′′ (1) < f ′ (1) 3. f ′′ (1) < f ′ (1) < f (1) 4. f ′′ (1) < f (1) < f ′ (1) 5. f (1) < f ′ (1) < f ′′ (1) 6. f ′ (1) < f (1) < f ′′ (1) 003 10.0 points 1 Let f be the function defined by f ( x) = 1 + x 2/3 . Consider the following properties: A. has local maximum at x = 0 B. concave down on (−∞, 0) ∪ (0, ∞) Which does f have? 1. A only 2. B only 3. neither of them 4. both of them 002 10.0 points When Sue uses first and second derivatives to analyze a particular continuous function y = f (x) she obtains the chart y′ x < −3 + x = −3 4 0 −3 < x < 0 − x=0 1 −1 0<x<2 − x=2 −1 DNE x>2 + y y ′′ − − + + Which of the following can she conclude from her chart? A. f is concave down on (−∞, 0). B. f has a point of inflection at x = 0. C. f is concave up on (0, 2). 1. none of them 2. A and C only The graph of a twice-differentiable function f is shown in 1 3. all of them 4. B and C only 5. B only Which one of the following sets of inequalities is satisfied by f and its derivatives at x = 1? 1. f ′ (1) < f ′′ (1) < f (1) 6. A and B only 7. C only myers (nmm698) – HW10 – Hamrick – (54868) 8. A only 004 10.0 points 1. 2. 3. 4. 5. 6. 2π π ,− 3 3 5π π − ,− 6 6 2π π −π , − , − ,π 3 3 π 2π , 33 π 5π , − ,π −π , − 6 6 π 5π −π , , ,π 6 6 007 10.0 points 2 − Find the interval(s) where f (x) = x4 − 5x3 − 36x2 − 5x + 2 is concave down. 1. 2. 3. 4. 5. −∞, − 3 , 2 4, ∞ 3 − ,∞ 2 −∞, −4 , 3 − ,4 2 −∞, 3 , 2 When the graph of f is 4, ∞ 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 3 −4, − 2 005 10.0 points x−1 x2 + 8 6 4 2 −6 −4 −2 −2 −4 −6 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Which one of the following properties does f ( x) = have? 1. local min at x = −4 2. local max at x = 2 3. local min at x = 2 4. local min at x = 4 5. local max at x = 4 6. local max at x = −4 006 10.0 points 2 4 6 8 10 which of the following is the graph of f ′′ ? 7 6 1. 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 4 −4 −4 -7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 4 8 is decreasing. Determine the interval(s) in [−π, π ] on which f (x) = 2 cos x − x myers (nmm698) – HW10 – Hamrick – (54868) 8 7 6 2. 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 3 4 −4 −4 4 8 3. (−∞, −3] , [0, ∞) 4. (−∞, −3) , (3, ∞) 5. [−6, 0] 6. [−3, 0] 009 10.0 points 7 -7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 6 3. 5 4 4 3 2 1 0 -1 −4 4 8 -2 -3 -4 −4 -5 -6 -7 -8 8 -7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 7 6 4. 5 4 4 3 2 1 0 -1 −4 4 8 -2 -3 -4 −4 -5 -6 -7 -8 7 -7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 6 5. 5 4 4 3 2 1 0 -1 −4 4 8 -2 -3 -4 −4 -5 -6 -7 -8 -7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 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 has exactly 2 local maxima, f has exactly 2 inflection points, f ′ (x) < 0 on (1, 3). 1. none of them 2. B and C only 3. all of them 4. B only 5. A and B only 6. C only 7. A and C only 008 10.0 points Find the interval(s) where f ( x) = x 3 + 9 x 2 + 8 is increasing. 1. (−∞, −6] , [0, ∞) 2. (−∞, −6) , (6, ∞) myers (nmm698) – HW10 – Hamrick – (54868) 8. A only 010 Determine if x → −∞ 4 10.0 points 5 2 7 2. limit = 2 1. limit = 3. limit does not exist lim 4x 6x + x−1 x+1 4. limit = 5 5. limit = 7 6. limit = 0 013 10.0 points exists, and if it does, find its value. 1. limit = 10 2. limit = 11 3. limit = 9 4. limit = 13 5. limit does not exist 6. limit = 12 011 Find the value of x→∞ Find all asymptotes of the graph of y= 3 x2 − 3 x − 6 . 3 x2 − 9 x + 6 1. vert: x = 1, horiz: y = 1 2. vert: x = 1, horiz: y = −1 3. vert: x = −1, horiz: y = 1 4. vert: x = 2, horiz: y = 1 5. vert: x = −2, horiz: y = −1 014 10.0 points 10.0 points lim 2 + 3 x + 4 x4 . 3 − 5 x3 1. none of the other answers 2. limit = 2 3 3. limit = −∞ 4. limit = − 4 5 Which function could have 5. limit = ∞ 6. limit = 0 012 10.0 points 2 3π 4 3π 2π Determine if the limit √ √√ x ( x + 6 − x − 1) lim x→∞ exists, and find its value when it does. as its graph on [ 0, 2π ]? myers (nmm698) – HW10 – Hamrick – (54868) 1. f (x) = sin x sin x 2. f (x) = 2 + cos x 3. f (x) = − 4. f (x) = sin x 2 + cos x 5 3. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 5 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 sin x 2 − cos x sin x 5. f (x) = cos x − 2 6. f (x) = − sin x 015 10.0 points 5 Which of the following is the graph of f ( x) = x2 ? x2 − 4 4. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 Dashed lines indicate asymptotes. 6 5 1. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 5 4 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 6 5 5. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 2. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 4 myers (nmm698) – HW10 – Hamrick – (54868) 6 5 6. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 6 4. 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 5. 016 10.0 points Which of the following is the graph of f ( x) = x + 1 x2 6. when dashed lines indicate asymptotes? 1. 7. 2. 8. 3. 017 10.0 points Determine which of the following graphs myers (nmm698) – HW10 – Hamrick – (54868) could be that of f ( x) = 1 + 2 x2 . 1 + x2 (iii) (iv) 4 3 1.2 1 0 -1 -2 -3 -4 4 3 2.2 1 0 -1 -2 -3 -4 4 3 3.2 1 0 -1 -2 -3 -4 4 3 4.2 1 0 -1 -2 -3 -4 6 5 5.4 3 2 1 0 -1 -2 7 f ′ (2) = 0 , f ′′ (x) > 0 on (1, 3) . 1. 2 −4 −2 2 −2 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 2. 2 −4 −2 2 −2 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 3. 2 −4 −2 2 −2 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 4. 2 −4 −2 2 −2 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 018 10.0 points 4 2 −4 −2 2 4 Sketch the graph of a function f that has all of the following properties: (i) (ii) f (x) = f (−x) , x→∞ lim f (x) = 2 , -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 myers (nmm698) – HW10 – Hamrick – (54868) 3 8 6.2 1 0 -1 -2 -3 -4 2 −4 −2 2 −2 10.0 points 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 019 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 Find the rational function f so the figure below is the graph of y = f (x) on [−8, 8]. 6 4 2 −6 −4 −2 2 −2 −4 −6 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 4 6 1. f (x) = 2. f (x) = x2 + 5 x − 6 x−3 x2 + 5 x + 6 x2 − 9 x2 + 5 x − 6 3. f (x) = x2 − 9 4. f (x) = 5. f (x) = 6. f (x) = x2 − 5 x + 6 9 − x2 x2 − 5 x + 6 x2 − 9 x2 + 5 x − 6 x2 + 9 ...
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