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

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