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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
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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!
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 Winter '07
 Osserman

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