More derivatives!-problems-1

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

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

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

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 ...
View Full Document

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.

Ask a homework question - tutors are online