More derivatives!-problems-1

# More derivatives!-problems-1 - handa (nh5757) – More...

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Unformatted text preview: handa (nh5757) – More derivatives! – bormashenko – (54880) This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – ﬁnd all choices before answering. 001 1 4. 2 10.0 points 1 Sketch the graph of a function g for which g (0) = 1, g (0) = −4, 2 1 g (1) = 0, 2 1 while 1 2 g (2) = 2 . 5. 1. 2 2 1 1 1 2 6. 2. 2 2 1 1 1 2 002 3. 10.0 points Find an equation for the tangent line to the parabola y = 7 x2 − 5 x 2 1 at the point P (1, y (1)). 1 2 1. y = 9x − 7 2. y = 8x − 6 handa (nh5757) – More derivatives! – bormashenko – (54880) 2 is the graph of a function f on (−7, 7), which of the following is the graph of its derivative f? 3. y = 10x + 8 4. y = 8x + 6 5. y = 10x − 8 6. y = 9x + 7 003 10.0 points If f is a diﬀerentiable function, then f (a) is given by which of the following? f (a + h) − f (a) I. lim h→0 h f ( x) − f ( a ) II. lim x→a x−a f (x + h) − f (x) III. lim x→a h 1. I, II, and III 2. I and II only 3. I and III only 4. II only 5. I only 004 10.0 points When 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 10 8 6 4 2 −6 −4 −2 2 4 6 6 5 1. 4 3 2 1 0 -1 -2 -3 -4 -5 4 3 2. 2 1 0 -1 -2 -3 -4 -5 -6 -7 5 4 3 3. 2 1 0 -1 -2 -3 -4 -5 -6 -7 4 3 4. 2 1 0 -1 -2 -3 -4 -5 -6 -7 7 6 5 5. 4 3 2 1 0 -1 -2 -3 -4 -5 6 4 2 −6 −4 −2 −2 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 −4 4 2 −6 −4 −2 −2 −4 −6 4 2 −6 −4 −2 −2 −4 −6 4 2 −6 −4 −2 −2 −4 −6 6 4 2 −6 −4 −2 −2 −4 handa (nh5757) – More derivatives! – bormashenko – (54880) 6 5 6. 4 3 2 1 0 -1 -2 -3 -4 -5 3 3. I only 6 4 2 −6 −4 −2 −2 4. II and III only 2 4 6 −4 005 5. II only 10.0 points For what function f and number a is the limit 2x − 16 lim x→4 x − 4 the value of f (a)? 1. f (x) = x4 , 2. f (x) = 21/x , 4 a=2 a=4 3. f (x) = 2 , a=2 4. f (x) = 2x , a = 16 5. f (x) = 2x , a=4 6. f (x) = 1/x4 , 006 h→0 10.0 points f (4 + h) − f (4) = 2. h Which of the following must be true? I. f is continuous at x = 4. II. f is diﬀerentiable at x = 4. III. f is continuous at x = 4. 1. I and II only 2. I and III only 10.0 points Below is the graph of a function f . 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 8 6 4 2 −6 −4 −2 −2 2 4 6 −4 a = 1/16 Let f be a function such that lim 007 Use the graph to determine all the values of x in (−6, 6) at which f is not diﬀerentiable. 1. x = −3, 2 2. x = −3, 0, 2 3. x = −3 4. x = −3, 0 5. x = 0, 2 008 10.0 points The ﬁgure below shows the graphs of three functions of time t: handa (nh5757) – More derivatives! – bormashenko – (54880) 4 1. all are true 2. B and C only 3. none are true 4. C only t 5. A and B only 6. B only 7. A only One is the graph of the position function s of a car, one is its velocity v , and one is its acceleration a. Identify which graph goes with which function. 1. s: v: s: v: a: 010 10.0 points If P (a, f (a)) is the point on the graph of f ( x) = x2 + 5 x + 7 a: 2. 8. A and C only at which the tangent line is parallel to the line y = 2x + 2 , 3. s: v: a: 4. s: v: a: 5. s: v: a: 6. s: v: a: 009 10.0 points Let f be a function such that lim f (1 + h) = 2 , h→0 and f (1 + h) − f (1) lim = 3. h→0 h Which of the following statements are true? A. f (1) exists , B. f (1) = 3, f (1) = 2 , C. f is continuous at x = 1 . determine a. 1. a = − 3 2 2. a = −2 3. a = 0 4. a = −1 5. a = − 1 2 011 10.0 points If the tangent line to the graph of y = f (x) at the point (6, 1) passes through the point (4, −9), ﬁnd f (6). 1. f (6) = 7 2. f (6) = 1 handa (nh5757) – More derivatives! – bormashenko – (54880) 3. f (6) = 5 4. f (6) = 8 5. f (6) = 6 012 10.0 points For what function f and number a is the limit √ 5 32 + h − 2 lim h→0 h the value of f (a)? 1. f (x) = x1/5 , 2. f (x) = 1 , x a=2 a=2 3. f (x) = x1/5 , 4. f (x) = a = 32 1 , x5 5. f (x) = x, 6. f (x) = x5 , a = 32 a=2 a= 013 1 32 10.0 points 10 8 6 4 2 −4 −2 −2 2 4 10 9 2. 8 7 6 5 4 3 2 1 0 -1 -2 -3 11 10 9 3. 8 7 6 5 4 3 2 1 0 -1 -2 -3 10 9 4. 8 7 6 5 4 3 2 1 0 -1 -2 -3 If f is a function having 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 10 9 1. 8 7 6 5 4 3 2 1 0 -1 -2 -3 6 as its graph, which of the following could be the graph of f ? 10 9 5. 8 7 6 5 4 3 2 1 0 -1 -2 -3 10 8 6 4 2 −4 −2 −2 24 6 24 6 24 6 24 6 24 6 10 8 6 4 2 −4 −2 −2 10 8 6 4 2 −4 −2 −2 10 8 6 4 2 −4 −2 −2 10 8 6 4 2 −4 −2 −2 014 10.0 points 5 handa (nh5757) – More derivatives! – bormashenko – (54880) 6 5 4 4. 3 2 1 0 -1 -2 -3 -4 -5 -6 If f is a function having 6 5 4 4 3 2 2 1 0 -1 -2 −4 −2 2 4 -4 −4 -5 -6 as its graph, which of the following is the graph of the derivative f of f ? 6 5 4 1. 3 2 1 0 -1 -2 -3 -4 -5 -6 3 2 1 0 -1 -2 -3 -4 -5 -6 2 −4 −2 −2 2 4 2 4 −4 5 3 2 1 0 -1 -2 -3 -4 -5 -6 4 2 −4 −2 −2 −4 015 4 2 −4 −2 −2 2 4 2 −4 1 −2 4 −1 1 2 −2 4 −4 which of the following is the graph of its derivative f ? 5 4 3. 3 2 1 0 -1 -2 -3 -4 -5 -6 4 1. 2 −4 −2 −2 −4 2 −1 2 −4 −2 −2 10.0 points If f is a function on (−2, 2) whose graph is 5 4 2. 4 4 5. −2 -3 6 2 1 2 4 −2 −1 −1 −2 1 2 handa (nh5757) – More derivatives! – bormashenko – (54880) 2. 2 1 −2 −1 −1 1 2 1 2 1 2 1 2 1 2 −2 3. 2 1 −2 −1 −1 −2 4. 2 1 −2 −1 −1 −2 5. 2 1 −2 −1 −1 −2 6. 2 1 −2 −1 −1 −2 7 ...
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## This note was uploaded on 11/21/2011 for the course M 408N taught by Professor Gualdini during the Spring '10 term at University of Texas at Austin.

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