Unformatted text preview: Methods of Calculus, Test 1P January 30, 2002 Instructions: Write your complete solutions in your exam book. Do not write on
this paper. This is a closedbook test. No calculators are allowed to be used. You
are not required to simplify your answers.
(1) (15 pts.) The following refer to the curve
, where )¡
98§
©32¥65£
)4
©4
7§6¥5£
©)¥
32¦£
1) §& $ #§ § ¡ © ¥
0("'%"!¨§¦£
© ¥£ ¡
¨§¦¤¢ (a) Compute
. (b) Find
. (c) Compute
of the tangent line at the point where
. . (d) Find the equation (2) (10 pts. each) Find the derivatives of the following functions.
(a) # I ¥V ¡ ¥
Y© S !X7W%© S UT
#§ §I $ I) ¡ © ¥
) $R#Q"'PH%¨§¦£
§G$ # § F %¨§¦£
¡© ¥
DC A § ¡ © ¥
[email protected]%¨§¦£
(b) (c) (3) (20 pts.) The position of a moving object at time (in hours) is given by
, where the position is measured in kilometers.
(a) Find the velocity function
.
(b) Find the acceleration function
.
(c) Compute the average velocity for the time interval
.
(d) Compute the velocity when
.
(e) When is the velocity equal to 0? S b ¡S
©S¥ a S `
©¥ cS c
I Rd¢b &¡ ¥
re© b ¦£
)¡ ¥
fe© b ¦£ (4) (10 pts.) Sketch the graph of a function having the properties:
,
,
for all . , § b u7§6¥£ §
b s¨§¦£
t© 4
p©¥
b q¨§h4 £ b ih6¥£ gH6&¦£
p© ¥4
¡ ©& 4 ¡ © ¥ (5) (10 pts.) Sketch the graph of a function having the properties:
,
for all ,
for all ,
for all , the axis is a
horizontal asymptote. § § © ¥£ ¡
¨§¦98 b (¨§h4 £ §
p © ¥4 (6) (15 pts.) Refer to the graph of
shown below. Answer the following. (a) The interval in which the function is increasing. (b) The interval
in which the function is decreasing. (c) The interval in which the function
is concave up. (d) The interval in which the function is concave down.
(e) The relative maximum point. (f) The relative minimum point. (g) The
inﬂection point. (h) The horizontal asymptote. v y x
wiX¦v 5
4
3
2 1 2 3 4 5 6 7 8 9 w 1
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 Spring '08
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 Calculus, Derivative, pts, Mathematical analysis, horizontal asymptote, Convex function, relative minimum point

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