Sol-165E3-F2007

Sol-165E3-F2007 - MA 165 EXAM 3 Fall 2007 Page 1/4 NAME GR...

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Unformatted text preview: MA 165 EXAM 3 Fall 2007 Page 1/4 NAME GR ING E7 10-digit PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10—digit 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. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. 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. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators, or any electronic devices may be used on this exam. (10) 1. Find the absolute maximum and absolute minimum values of the function I f($) = $24 on the interval [—2, 4]. m2+4 numb—MS? £/( ' (XZ+4..)27( -- (Xz’4)2)( __ z, X)’ 0844)" a UZ+4) g’(x):02 £1,220 —-—7 7:20 (1) [x‘+4 ._..16-—‘i’ _ 1.2, I, 3 _,.._ "‘ 46+4 ’E’“ "3:. abs. min. f(0)=-'1 9 £0» :’L abs. max. ‘ + G) (10) 2. Suppose that the function f is continuous on [~3, 5] and differentiable on (—3, 5). If f(5) = 12 and —1 g f’(a:) g 2 for a: E (—3, 5), What is the smallest possible value of f(—3)? . (5% ('3) _ I Y — 5 Ram Meow \Iw vaem. iE:%§,£(c)® ,Lo 3w ce(3,) Sim». —1 f 5/60 52.)}.1'3 lie-$932 32 e «(as 12 — €637 $46 -205 —§(*3)f4 202 “133-4 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) : 07 and f’ changes Sign from positive to negative at 3. Using the (N?C rs rvative tes second derivative test we conclude that f has 6 local maximum at 3 l a local minimum at 3 no local maximum or minimum at 3 (6) 4. Find the rc—coordinates of the inflection points of the graph of f : 3x5—5$4+2:1:+1. 5/(X): 157(4p-ZOX3-‘f'2 g (x) = go x _.60'x : 60x(x-1) §//(X) : Lid—3% W—‘i )r o “L (24) A; 5. Find each of the following as a real number, +00, —00, or write DNE (does not exist). vi (a) 1m “W 5:? Kim M: a” g maxl$ xfiw 1 LI” ' g g g: 0° '::‘2.L"rn [my :QLW 1:0 [EL g 'X">°° 'X 3- 3‘ .29. ’ 00 g n l r 2 O 11 + —— m X .— __,m 'm ‘:= y A \ 'm X 1: _’ Do ‘_____ a m- in 7:. _ 1 — Sins: Ly __ S L’H . 1 ‘4 (C 9313]]?(15— 92 2 by” C0 7 ‘2 Law» 2%?" 3'72: :3 o 76"; 20‘"; 7—”; Q, —-—-“ 0 9 _... ‘1. g; 0 o '2" E] (d) 11m (1 g 239% +\ “0+ ; . £"(1—2wf" Q“. a i bow” @ ‘1 {m (1—zx Wrfl/nm e = 7170*. xaod’ 7‘6 + “i 2* €93°*%‘“2“("” @ e: b *2 QM [nu—2x 1:3 Rim fig:~2 MA 165 EXAlVl 3 Fall 2007 Page 3/4 Name: (18) 6. Let f($) = 1. Give all the requested information and sketch the graph of the function on the axes below. Give both coordinates of the intercepts7 local extrema and points of inflection7 and give an equation for each asymptote. Write NONE where y NFC l“ avoid" appropriate. Dawwu‘n', QM “$0 2 _ Xqfii Lézo —4 X's'l. la—l'nt. MM- Sfimmé1x‘3 FLOYLL 7r—wo 7(2 . x -1. ._ (.4 W7 "if " W ’9—00 Ha“ as a, domain ‘6- ' m —; .—-oa intercepts x-—>0* XL . X -) b m - 2" Z _ oo symmetry x~a0 7i horizontal asymptotes x4 vertical asymptotes ~x‘ «ax : __ _:_12_ I X4 0 1 intervals of increase gcx) ‘---;T++i‘+lfi"‘ —>K Q7 3: intervals of decrease Lac ma X {/1 )_ X . .1. «(X—2)?) x1 local maxima x - x6 ,7... '2 13+ 5x1_ 2 7‘ ’3 local minima c " X4 X ’80 _. .. _. _ ,_____o++ *fintervals of concave down 3 X ,1 intervals of concave up f)?“ 0/ I'M/1.1 (3 3;) ) ’9 points of inflection Fall 2007 MA 165 EXAM 3 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/f9, the material for the sides costs 10 cents/ft27 and the material for the top costs 20 cents/ftz. Determine the dimensions of the box that can be constructed at minimum cost. (Let :1: denote the length of a side of the base and 3/ denote the height ofthe box). x1 :20 @ C051: ' C : X330) + 4"'><~3(10) + 78(20) @ - ‘20 El“ “'5: @ C —.— 5m" + $9.9 , o<>< X 2‘5: 1007c _ 800 @ ELL—o 100a:— ‘ELO -o —->><——8 ~>w=2 our ' xz' d5: - ——» O +++ 2-D- * ° ,2 ‘9‘ 7'5 @ fl *1)?" 33: affiy=5Ft (6) 8. Find the most general antiderivative of . z_ 2 f(33)=Sln$+3e W -1, F1: +ov musing) +C (6) 9. Find f(t) if f’(t) = 2cost +sec2 t, —% < t < %, and : 4. §(t) : 281M? +T0mt 'l' C - . __ ‘ 7r )1 Dal—31. 4. -ZSm—g+ liar)? 'l—C 4': 2g+G+C ‘ Ct4—2‘fi ...
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Sol-165E3-F2007 - MA 165 EXAM 3 Fall 2007 Page 1/4 NAME GR...

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