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Unformatted text preview: MA 165 EXAM 3 . Fall 2007 Page 1/4 NAME
Ill—digit PUID
RECITATION INSTRUCTOR ___  RECITATION TIME DIRECTIONS 1. 9° (10) 1. (10) 2. Write your name, 10digit PUID, recitation instructor’s name and recitation time in
the space provided above. Also write your name at the top of pages 2, 3 and 4. The test has four (4) pages, including this one.
Write your ansWers in the boxes provided. You must show sufﬁcient work to justify all answers unless otherwise stated in the
problem. Correct answers with inconsistent work may not be given credit. Please
write neatly. Remember, if we cannot read your work and follow it logically, you may
receive no credit. Credit for each problem is given in parentheses in the left hand margin.
No books, notes, calculators, or any electronic devices may be used on this exam. Find the absolute maximum and absolute minimum values of the function
f(a:) = 5% on the interval [—2,4]. abs. max.
abs. min. Suppose that the function f is continuous on [—3, 5] and diﬂerentiable on (—3, 5). If
f (5) = 12 and —1 S f’ (51:) S 2 for :L‘ E (—‘3, 5), what is the smallest possible value of f(*3)? MA 165 EXAM 3 Fall 2007 Page 2/4 Name: (6) 3. Circle the correct answer in each of the boxes. Suppose that f” is continuous near 3,
f” (3) = 0, and f’ changes sign from positive to negative at 3. Using the ﬁrst derivative test second derivative test we conclude that f has a local maximum at 3 a local'minimum at 3 .' no local maximum or minimum at 3 (6) 4. Find the az—coordinates of the inﬂection points of the graph of f (x) = 3x5 —5:174+2a:+1. x: (24) 5. Find each of the following as a real number, +00, ~00, or write DNE (does not exist). (a) lim (111$?
$—)OO :L' (d) lim (1 — 233% x—)O+ MA 165 ' EXAM 3 Fall 2007 ' Page 3/4 Name: 33—1 (18) 6. Let f (:17) = $2 . Give all the requested information and sketch the graph of the function on the axes below. Give both coordinates of the intercepts, local extrema and points of inﬂection, and give an equation for each asymptote. Write NONE Where
appropriate. 3/ symmetry . horizontal asymptotes
vertical asymptotes ’ i
intervals of increase ’ intervals of decrease local maxima
intervals of concave down l:::l
intervals of concave up l::::
points of inﬂection :: MA 165 EXAM 3 Fall 2007 Page 4/4 Name: (14) 7. A box with square base must have a volume of 20 ft3. The material for the base costs
30 cents/fizz, the material for the sides costs 10 cents/ftz, and the material for the top
costs 20 cents/ftz. Determine the dimensions of the box that can be constructed at
minimum cost. (Let 3: denote the length of a side of the base and y denote the height of the box). (6) 8. Find the most general antiderivative of 2
\/1—$2 f(a:) = sinx+ 36$ — (6) 9. Find f(t) if f’(t) = 2cost+seczt, —% < t < %, and ﬁg) 2 4. ...
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 Fall '08
 Bens
 Calculus, Geometry, recitation instructor, Recitation Time

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