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Math16Amid2sol

# Math16Amid2sol - LL Math 16A{Full 2mm)1 Kirkbride Midterm...

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Unformatted text preview: LL\' Math 16A {Full 2mm _ )1, Kirkbride. Midterm ‘2 Please PRINT your mune here : Your Student ll) Numher: 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. PLEASE KEEP YOI'R OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EN.\.\I SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOI,’ FOR YOUR COOPERATION". 3. No notes. hooks. or elnssmutes may he used as resources for this exam. 4. Read (liroet ions to each prohlem (,m'efully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a. good score on this exam. Nentness and organization are also important. 5. Make sure that you have .3 pages. including the cover page. 6. You may NOT use L'llopital's Rule on this exam. 7. You may NOT use shortcuts for ﬁnding limits to inﬁnity. 8. You will he graded for proper use of limit. notation. 9. Put units on etusn’ers where units are zmpropriute 10. You have until .‘lztltlpm slmrp to finish the exznu. ‘i 1. Compute the derivative as indicated. Do NOT simplify (\ p15 midi). a) Find f’(1‘) if f(1) : (3m -— 5) * J? 9/04”“: u" rum: " ' ‘ ‘1 {‘(‘d .; g5! 4 (3ch’23 ' \ILX ’1 b) Find f”(ac) if f(1') = 3.1% +1- tanw c Find ’if = ) y y «m Qvuﬁ‘ni' gnu: ”/1 . I _‘ 6&7—1 ~ \iXH 5 - +Ov~X '- ‘ILLXL+?)) . Ax J " Kiixl‘rfi )1 . dy .. i d F — ’2 .' ."‘—-;' ) 111d dry 1fy 005(1 11) 45 ’53 s —s'¢n(x3~‘6x3 - (3x1. 4) ‘2. (.6 pts) Find the absolute llleleII’lllln and minimum values on [1, 2] for the function i 2 1 Z . . ((YL\ : l/l‘f +-;~ T; : J, 4 ‘1 :" Lft’b' (liklu’c§x+(';{L) Q q {twawa 6!; .32 (at «mitt?— Line‘s 71: XL x7"« (m ~ l+Q=3 ‘3!” : QLxI") \\ ///‘+_ ~ X’ __:__f+.:___. mMetzi. 6') X‘= ‘ (Nix ‘2 hi3) 7 . '~ 3. (’0’ pts) Assume that the SECOND derivative of function ﬂat) is f”(x) ‘l: x4 —- x3 —6ZB2. a) Dt‘lt‘l'llllllt‘ tlw .r—vuhws for which f has inﬂection points. a —.= x“-x‘»w1 x=.x,3,~oz OaxLUix-c) 4, I__ + .. a 1 o 72 mm PM {infuwgﬂ b) State the open intervals on which f(1') is concave up or concave down. Qongmv‘g UP: F ’9‘ ,"-"—2) k)(%\.m) A , . kcrx ('c‘V'i’ dOV‘U/‘f ( .— Q . 3) 7. , . ¥ t l. (‘44 pts‘) You 2m» standing on top of an 80 ft tall tower. You throw a rock straight up with velocity (ill t’t/sec. How fast. is the rock traveling at the moment when it hits the gi'ouiul'.’ ‘ \mm ; not“ + UH 4 can Q we) = - 5Q+ HoLi ind) : «ab-gut + 8+ + m) kg”): - lb(41“‘l*l ‘5) —. ~\u(+1~tt+-5) , (+—<3)(++t) #:igﬁiivi i x ‘3 \n'(5\c -(?>X3a) +3 (0%: «wt/mi \{ v,\ o6 t l» "\ ,2 3. 1% pts) Consider the function f(:1:) = ,3. .7; ~ I a) Compute the FIRST (.lerivative ‘ . 1 A; (’(U: 3XLX~3l ‘ x (i) Qx”~\ov»x7‘ N:- - 7. . (1‘3) gm» .9" a x’ I; "M A x (204.) Liv 1) )1. Cﬁ—S) I. h) Set up a sign chart for f’. Identify relative exti‘oinn. i11('l11(lil|f; y-mllios. F i, .4. __ + M a x (i)! O ) ‘W m‘x‘ (VH1) )(‘D c [1'3 {1" :3: 0 VA s3=u (3) State the open intervals on which f is increasing or (l(‘,('l't‘:l>lll};. lnu‘cqs; If) (”’53: ,0) U L \a l 0») AW «33 (o. 3) o( 5.5) 6. (10 pts) Graph the function f(:1))‘= :17“ — 3.153 including ;r mwl 1/ intercepts, relative extrema, points of inﬂection, and asyniptotos. You are given that f’(;v) 2 3x2 ”6.17 and f”(.z") = 61' — 6. i (‘0) »~ ‘Sx’Ew ' O ‘3 il)x(X-3\) ‘bi :Q ‘50 o3=*l-I l ru Maw. FM pm. 7‘ t 1 his) Sketch the graph ot‘ a function which is continuous at the point a: = 2 but NOT (liti't‘rt'utinhh' £11 .1' r“: '2‘ I- ‘ y ‘H'N’iL‘vS" 8. EXTRA (‘REDIT (4 pts): Consider the function whose derivative f’(a:) is given in the «graph hvlow. REMEMBER. this is the graph of f’(1‘). However, answetr the following questions about f(.l). NOT f’(.1;). ‘ a) List lllt‘ x—vuhu‘s where the graph of f(3‘) has 21 relative maximum. , ‘ ,< r} if‘ 5% i=~11| “-3 ~‘3 l 15' 1)) List the x~mluvs where the graph of _f(;r) has an inﬂection point. \uul'wk 61% of 0M NdHL/x studs 1‘”; x=~5,~i,3 ...
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Math16Amid2sol - LL Math 16A{Full 2mm)1 Kirkbride Midterm...

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