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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online