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Unformatted text preview: handa (nh5757) – More derivatives! – bormashenko – (54880)
This printout should have 15 questions.
Multiplechoice questions may continue on
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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.
 Spring '10
 Gualdini
 Derivative

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