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Unformatted text preview: MATH 1241
COMMONFINAL EXAMINATION
FREE RESPONSE SECTION
SPRING 2002 This exam is divided into two parts. These pages contain Part II which consists of
6 free response questions. ' Please show all of your work on the problem. We will not grade loose paper. a If you are basing your answer on a graph on your calculator, sketch a picture
‘ of your graph on'your sheet and be sure to label your window. 0 Make sure that your name appears on each page. 'At the end of the examination you MUST hand in this test booklet and all scratch
paper. FREE RESPONSE SCORE: Name: . ' ‘ rrStudentNo: Instructor: ' Section No: MATH 1241 FINAL EXAM ‘ Spring 2002 PART H 1. For a'certain function f , the following information is known:
i. f is continuous, and has continuous ﬁrst and second derivatives for all x.
ii. f’(:r:) < 0011 ( — oo, 0) and f’(:c) > 0 on (0,00).
iii. f”(a:) < 0 on ( — oo, — l) and (1,00); f”(a:) > O on (  1,1).
wn—u= —1n0>=—zﬂw=—
v. mlir_n oomﬁ )  l1rnf( ) Use this information to answe1 the following questions: (a) Determine where f is increasing and where f is decreasing, and ﬁnd any local
extreme points of f. (b) Determine where the graph of f 15 concave upward and where it is concave
downward and ﬁnd any points of inﬂection. (0) Sketch a curve which could be the graph of f. MATH 1241 . FINAL EXAM 7 Spring 2002 2. (a) HP : (a), y) is a point of the line 9 : 3:13 + 8, and D is the distance from P
to the origin, ﬁnd a formula for D2 as a function of m. (b) Determine the value of :1; which minimizes D2. (c) Explain how you know that the value given incpart (b) really does
minimize D2. ' ((1) Which point of the line y = 33: + 8 is closest to the origin? MATH 1241 FINAL EXAM Spring 2002 3. Find the absolute maximum value and the absolute minimum value of the function
f (ac) : $239 on the interval [1, 5]. ' 4. On the given graph of the function f , choose a positive value for h and mark line
segments which represent ’ 1 f(3)
ii. f(3 + h)
in. £(3 +11) — f(3) Also,
, v. draw a line segment whose slope is W. [For each of i, ii, iii, iv, v, make sure you clearly indicate which is the appropriate
segment] 7/ MATH 1241 F WAL EXAM Spring 2002 5. Assuming that f and g are differentiable functions, ﬁnd the derivatives of the
following expressions: ‘ 1172 + f(503) — 9(964) ii. cos (g(a:))  eﬂx) 6. A particle in motion is moving along the a: — axis in such a manner that its position at
time t is given by __ 2t _ 1 + t2 9:05)
where a: is measured in meters and t is measured in seconds. i. .Find the velocity at time t. ii. _F or which time t > 0 will the particle come to rest? iii. What is the velocity at time t = 2 ? iv. For which positive values of t is the particle moving to the right? ...
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 Spring '08
 XIU

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