Practice_Final_Solutions

# Practice_Final_Solutions - PRACTICE FINAL EXAM MAT 21A NAME...

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Unformatted text preview: PRACTICE FINAL EXAM MAT 21A NAME: DIRECTIONS: Read the directions carefully before beginning. Gom‘l Luck! 0 This exam is a closed book, Closed notes. Nothing should on the table except a pencil, an eraser. and this exam. 0 NO CALCULATORS or other PAPERS allowed. 0 Show all work, clearly and in order. 0 When required, do not forget the units! 0 Circle your ﬁnal answers. You will loose points if you do not Circle your answers» l PRACTICE FINAL EXAM MAT 21A NAB/IE: i( E 1? Problem 1: SEE EXAM l. PRACTICE EXAM ll, ANT) EXAM ll FOR PRACTICE FOR CHAPTERS ‘2 AND 3. Problem 2: Find the dilfcrcntials for the following functions. PRACTICE FINAL EXAIVI MAT 21A NAME: (c) y : r:“.€iw(;c3), at :1: :E 2 4f Hg) 5 Qg’ﬁmﬁf): {2' E SY‘QF 2,23“ {HE (d) y 2 (40521111117:(6'2”), at .l' = (7) ms 2; 0 207 ),1Q ”"1 9(8: PRACTICE FINAL EXAM MAT 21A NAME: hi6 Problem 4: Find the absolute minimum and maxirmlm of the, Following funvtions on the npprt,)p1'iate domains. (21) 312.172 + 2117+14, 011 [M1, 1] S'Qyzlx‘r‘z, :1) (3) X3»; 56’» ‘1 (7)1":l H72". [3 5-())9 ){v’lH°[”)7 (b) y = 1;:()Il[—-2.2] (C) y — (WM/11(4), 011 [—n’, 7r] - ,, " r’I §"0)¢ﬁ(w&+60\$"> ’0 UM" X ~Eb '7 S (-70 :0 L \$(r7 SO ’1,- =- 4-3 Wax < Wﬁﬂ‘ '12:: >Q 51!” 9(3?) 5 647 (d) y : 63"”‘2(.I:2 — 4:17 + 4), on [—10, 10] M» z\) yo» 3 0, (m w Fm) w {G’b/X‘lﬁRXB 5-0 5> A \$2 (51")(4‘0 Sr (07 9 9161’ V 'm' 4’ H2)” 7 7 57 M75 m a gym) 5 87174) "' ﬂnD/refr ”04’" w) PRACTICE FINAL EXAM MAT 21A NAME: thugs Problem 5: Find the extreme values of the f(,)“(,)Wing functicms and use the second derivativv test to deterl‘uine if they are maxima, IIIiI’liIl‘l'dw or neither. 4 (a) y = 3;]:(17m -— 2) "03 = 384M454 3%.) z 306%,) 0 <9 XcL 5 ll )1 / S e, 3 3 8105: ;L :0 Nwahb, {we 04» V4 EM 3‘ Mg m m PRACTICE FINAL EXAM MAT 21A NAME: )Qﬁ Problem 7: State the Mean Valuv Thocwvm. Sag, Wm, Né’ces, (JV @230}- 3821’ (/2... Problem 8: Use the Mean Value ’J_‘heorem to ﬁne the point at which the slope of the tangent line to y z I” parallel to the line through y = :1)? at the endpoint of the interval [0. ‘2]. gm» Lam nah: or gook gen, a; Problem 9: For each of the following ﬁnd the function f(;1:) whose (.lerivativn is given and that passes through the given point. (a) f/(H') = 200.317, (0,3) g‘bi) CRYMXK 9(0‘733 2‘? (L63 -, (b) f’(;lt) : 4:1:3 +1: — 1 + HT, (0, 0) PRACTICE FINAL EXAM MAT 21A NAME: Problem 10: Give the intervals on Whi(‘i1 the following ﬁnwtinns are increasing and decn‘easing and indicate which are which (Hint: use the ﬁrst derivative test for monotonic functions). ~2 -1 4 g (D (73% o (b) y = emsiv‘zbr), 011 [02/7] 1 £2"): 338““ +603X>¢~Qf[§mx. ’“fasx> -: a a; A V ) 7 Problem 11: Give the intervals 011 w 1101 the following .. 1, . V , (rave up and concave down and indicate which are which (HM/s use the second derivaivo 1,031, for COHCEWiiy). -2 I/ ~ - (a)f(,r)=:r%. gléﬂs’éxé §G)¢'3;~xé )0 £0)" x<0 4‘) gear X>O ‘1+1r:' w PRACTICE FINAL EXAM MAT 21A NAME: Prublem 12: Use the ﬁrst and semnd derivatives to graph the following functions. (a) fur) :: .197. W {949 014 M )4,qu (b) NW) 2:174 — 405+ 10. gag/L q (/ (c) f(.1,~) = L12; 1+1“ ' Problem 13: In the text, exercises 1.5.7. (1.3.19, and 1.5.27 PRACTICE FINAL EXAM MAT 21A NAME: Lil? Problem 14: Use L’H(_)pita.l’s Rule to ﬁnd the f(,)H(,)wing, limits. (a) 17mm :)(:,—E—- s M ’ w» x c J M» ""4 5‘ =7 [m (L 5* — AC! ,0. )v-vo 33a?” X’ﬁo Q )1 X ’50 C , 0 95“ g (4% w SEE/«m #2- s “/5 x-‘ao ’3' 9. (b) limb”, 8' gnsr— l “ﬂ ' (0)177771,‘0’—”7.i £05K )6 X’AJO l g 0 ﬁﬂm f1» Xﬂml 9 [Z— (d) III,IT;)0) V . 2/620 ﬂX/X’Mfi X’qL) £011 [MZ/ ’5 00 ) Xaﬁ [MCXF3> )500 2,169) m; 32,003.13. 36 /. Z ,L .Q/MB :2 )c :’ IAAS ﬂm 3% :— ﬂVt’jﬂ/Dx ‘5 jW’ I c. .49.» (f) 17777,‘,,-;.,(~,; mm. + 1-) )'~. 773 4.9, ,L / (H—X) , E :, in :33 1 :ngol 009:“ a Lﬂﬁbm x Qxacﬁ”) 3 6 2& )k"5 egg- ...
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