Test 2 Key

Test 2 Key - Test #2 Math 141 Fall 2011 Version A Show all...

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Unformatted text preview: Test #2 Math 141 Fall 2011 Version A Show all your work and answers in your blue book. 1. (+16 pts) Find the equation of the tangent line to the curve y = Jr3 - 2x at the point (2, 4). 2. (+20 pts) Use the definition of the derivative to find the derivative of f(x)=1/3+5x 3. (+24 pts) Find the derivatives of the following functions. Do not simplify beyond finding the derivative. .l' 4 1 2 3. =2 +—-e‘+tan(3x) 3’ J} arccosx b. = y 3x5 c. y = ln(5x+ l)+ sin3 x d. xcosy = xay e. y = (sian a. Find h'(l), given h(x) = (f o g)(x) b. Find j'(2), given j(x) = 3f(x)+ g(x) 5. (20 pts.) Given the graph of the derivative of f, f '(x), answer the following a. Where is the function, f, increasing? b. Where is the function ,f, concave down? c. Where is the second derivative undefined? In other words, where is the above graph not differentiable? T‘s—t fi'Q—d UJMmq A I. 3:263” 34: (on—D ?;_,3y”~9_ 5L: [01*20+Ll Lg:(m:/O C zeovc—tLp) Q.ac(fl=1/3TSX_ i _ _ mfim_m+m M”??? h __ _ __ 5% 3%» M :% hao/(m +M) hag +JFE} : ‘3 &V3+SX ch -3} 3. 3!: ayina—fl 2- + (pXAJ-QZ—(SXZ') - Macmx (st‘f) — —~ I b) b_ ff— 519 3X (SX‘Y' C.) { -_: I -{- BUIMH'LX. Coax g /5x+r[ ‘0 ’ my“ M‘S‘WM’ ; axw xi? X251: ZSIflbL 8' :1” 52x3 —CO$&5'_ €) jj‘CAI \Dnj : 1 ,—-— 51., nyly X .Qfl\ub\r\¥\ Wainlamfl -+ I [105%. x Jinx 3‘ “’éofilmt “Co-*0} x : (inlmmJ ‘f X 00*”‘7 (Anya @ hi“) 3’ l(gtfl\ %ICU ’ :f[( H) (23 5 (“H (23 '3 ’2 Fan : 3. yaw CGQA v: 5(21 +3 1 a # I 0 @OD (’QJVI) U (Cg-2:“)? xiii/16.3% > come 010% In) (/9213 ,8, Con 2% Test #2 Math 141 Fall 2011 Version B Show all your work and answers in your blue book. 1. (+16 pts) Find the equation of the tangent line to the curve y =- x3 - 3x + 1 at the point (2, 3). 2. (+20 pts) Use the definition of the derivative to find the derivative of 1 f(x)=3+5x 3. (+24 pts) Find the derivatives of the following fimctions. Do not simplify beyond finding the derivative. a. y = 3" + %— e3 + sec(3x2) arcsin x 2):4 b.y= c. y = ln(3x +1)+ cos3 x d. x3 siny = xy2 e. y = (cos x)‘ 3. Find h'(2), given h(x) = (f o g)(x) b. Find j'(5), given j(x) = 3 f (x) + g(x) 5. (20 pts.) Given the graph of the derivative of f, f '(x), answer the following a. Where is the function, f, increasing? b. Where is the function ,f, concave down? 0. Where is the second derivative undefined? In other words, where is the above graph not difi‘erentiable? / {65+ a” ’VMKOfi15 f @ d a W %’X’3X+l 190er (afl’fh 56:3)823 5L—5:9(x~afl gm- uni/5 ‘3 7’ 9’”le :2 C1 AloPc, : @ t #1;- fl I ( = f __ I so 3A {:34 3+5Cx+m 3+Sx 5M3+sx+5h 3+5x h h—‘Do h -. “V5” ‘5“ .L _ . “5% hgo (3+3 6513*wa h“ fig? (3+5m50 {360 5 ,_ 5 ($591 m 5’ = Bxfirfi — :mf’i o +wacgmpcmam «ox — 3¥J1n3 _ aitlL—e— achCSxQfianCBXL§ I -— 0&0.sz (9X3) ‘~ a753, b) ‘2} ’ W (a? x“); a) y] : k (37 4— 3 CMLC‘D (-zdm K1- (BM—If c0 3x1.a\na,+ 763001635} 7— Lgf'k X‘Z‘a‘f I : kdf‘ ,_ 3781,6103, t 3 04 fl. : legxflsm 3 (7C a a, 376%) xilf'iawgraw/ _l_ ' M a) a Man: oc‘(%clfl-<g;(2> a;’(s)=330'(53+ cases) ~= 30133. (33 :3 (m + ~3 _ :1 “ll—3 @ in —Q U C 7315 inorem'm? Mm 51’ i5 Foé‘rh we... f’tfi COACOUQ (30er W Jler<O j aclis dCCFEMina_’ ...
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This note was uploaded on 11/08/2011 for the course MA 141 taught by Professor Wears during the Spring '07 term at N.C. State.

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Test 2 Key - Test #2 Math 141 Fall 2011 Version A Show all...

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