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M1550-Exam3-Sol

# M1550-Exam3-Sol - 11:11a Kg Math 1550(30 EXAM 3...

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Unformatted text preview: 11:11a- Kg)! Math 1550 (30) 11/04/2010 EXAM 3 Instructions: You must show your work to receive credit. Scratch paper will not be collected, so you must write all your work that you wish to have graded 011 the exam. No calculators! There are problems on both sides of the paper! Problem 1 [12 points] Given below is the graph of the derivative j" of a. function f. F00 Use this graph to ﬁnd: t . . . (a) The intervaﬂs) where f is increasing: (-413) U (5-,?) (where x IS PSlhve) (where S‘is neaad'ive) (b) The interval(s) where f is decreasing: (3 '5) (e) The interval(s) where f is concave up: 6— l, l) U (lg-IL) (where Q‘ is increasma) (d) The interval(s) where f is concave down: CMQU (5'4) (where «it I! '13 MM???) QM?" Karo Problem 2 [14 points] Find the minimum and the maximum of the function ﬁx) :52 — 2:: + 2 on the closed interval [0, 3] {‘00: 2.x..2 X \$00 \$004) I | 4—— mm 21*2 = O D 9. Xr-m Criﬁcai “ain't 3 5 ‘__ MX {‘03 = l—2+ 2=I . Coi— — 2. mm: 1]] Problem 3 =[l11 points] F ind the limits: I ' 14\$ _3; b). lim 30‘ £11.35 3; x—ﬂ 1 — cos(:c) W13" . \«qunsmg X =§ ﬁfe? l = (14') *JQM (3) z X = 11M 2X Wk i- a Problem 4 [13 points] Find the inﬂection points of the functi0n: f(3:) --- .123 — 9:52 +3. #00: 9X1—18x x m a n ‘1!”(Ki-‘6X-13 1:100 _____ 0 + + "(x =0 u . ‘ tab-:3 =0 ti Macs Sign a1"- So ‘Ulus 13 X = ‘5 an inﬂec‘ﬁon mint. Problem 5 [13 points] Find the critical puints of the function: ﬁx) 2 \$633. \$00 = e3“ + 3x (-13" = mm” 3m) =0 am.) (33:0 ItBK =—O Problem 6 [13 points] Find the intervals where f is concave up and concave down: f0”) ;.—_ 37 — 111(3) where m > G. 1 = _ _L t? 00 1 x fwd: JX: )0 ﬁnd“ 100 => .Q is commie 9? on (0,00), Problem 7 [9 points] Find two numbers A and B, with A S B, whose difference is 18 and whose product is minimized. B—Aam B:— AHB Prodllcf: T’ = BA = CA+1B)A s A23? 18A P’= 2A+I8 War-0 => ZAHX =0 =’* A= -‘? A 4 P’ -- 0 + + A=El P \M/ B=A+lB=—‘l+\[email protected] min Problem 8 [12 points] Match the functions with their graphs ~ place the letter corresponding to the correct graph in the box below each function: Bonus [10 points] Find the limit: 1- 21E] «1:330 1013+10 — 2 m. 20‘ EM. 1* 010x ‘8: km e "(Mt-Ho == Slim In 11-10 )= (lb tax 1" (Tl—o X—ru 1&(‘013‘10 =43: 2X M(10K+l0=%\$:2 J-XHO E. M’ D A 2- M mod: 2X” :- ‘M'L M (MTG) _ ' ‘0 __ ﬁe —2,ox .— "20 M“ -—! "£33 Know-10) xﬂ‘ {mum " “‘5‘ =63 ...
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