10.11.Solutions by hand WS 2.4

# 10.11.Solutions by hand WS 2.4 - MA 160 Section 2.4...

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Unformatted text preview: MA 160 Section 2.4 Worksheet Name (:2. C30; “fan Using Derivatives to Find Absolute Maximum and Minimum Values 1 1. Consider ﬁx) m x3 + Y2 ——2x+4 . "in a. Flnd fKX) Z :‘S bﬁzﬁ. x «A x (.33; "ﬁa‘istgrﬂ b. List ali critical values of f X "Ti 7-3119 c. For each given interval, complete the tabie and ﬁnd the absolute maximum sod minimum values of f on the given interval : (i) m {-29 9} Absolute minimum value x (critical values in interval and endpoints ) off2 :2, which occurs at X. m w 9'1 Absolute maximum value #4.,- 53} :- Li, off: 3 ""-, which occurs at Absolute minimum value :2 3; (critical values in interval off: which occurs at X: «s2 Absolute maximum value off: it? __.___.__.__._~_____) which occurs at 2. Find the absolute maximum and minimum values of f(x) = x4 ”- 2x3 on [—23] and indicate the vaiues of x at which each extremum occurs. Find f‘(x). we) : mime X mowed) Find all critical values: X355} x3335}. Absolute minimum value _ off a '“ who ___—_.,_,9 f which occurs at X = 3 Ila Absolute maximum value 3"; __——._J off: . which occurs at x r» '“ <2 For each of the following problems, ﬁnd the absolute minimum and maximum values of each function, if they exist, over the indicated interval. A130 indicate the value of x at which each extremum occurs. . a or? [wSﬁ] 4- f (X) m J; on [—8,1] Mk) V K "3 . .X ‘l’fflil tilt,”- (crltlcal values 3 and endpoints ) ﬂwv’wﬂ' d 04212;. ”‘1; KW ... a? mgmg-«g’zg: Absolute max. = Ll which occurs at x 2 "M 53’. Absolute max. “ l WhiCh occurs at X = I Absolute min. = 0 which occurs at 3:; ~—* 5) , Absolute min. = ”=3- which occurs at x = “"6?“ . __ _,_ 2 __ __ 50’? 5. f(x)— 2): +4036 270 on ( 00,00) 6. fU’}-\2+- (m (0,33) "Cid!“ :“q-Kv4di-W-“5 .. LfCKle) ll. x :2. an? ”r. . . ‘ . ,. . I » _, .' . - M. H - , , " a , a) Uwg’eez/Q VaW.M/K3L0 (3%” ’R'k*‘\$’b“‘(“53?‘ r- Al'veﬁ V ‘ . . ,_ . 9.55:4: {4.122.353.3de W/Wﬁewmﬁraaqﬂgga 2.3:,” .WEM; «p5,? lmeﬂﬁgﬁﬂg 1%)“; Meg give/avﬁmbi. ysézé’eee 32:. g; Sw‘mgw .37 (.9 ’1 '5 . "I... _ ' {ljiw ww'fl—fﬂvv é: _ K K 33.1.25“ “ijéé‘ﬁ; 3;: «£1453. M”[email protected]¢%‘ “€105; kjgdﬂmﬂﬂbgﬂﬁ “Egg! —~ W Cwéodi’}. .4quww. Jag; 43 {call :5 wide. ‘ (543‘) I: ”:2 ‘";3/t’§'¢> ﬂ» 1..) 36.13;: .1 er fig—3‘; W mescéé prtﬁ. 4?“ f ﬁfﬁazﬁ‘ 7” :5. ~ " {13,}: 3W.MM\ 3,14% é>WCéVX%QC'-Jqf 77% W m"? Mg’itrgwa ﬂ/I‘Lérlrb&;}' “It?” ’ x I I .7 if j . _. \ . ‘7 J? . T ”’7‘ ﬁiibg» «czéem xrmgmumyumﬁ wk; 4’55”} 3’75f , 2 . .. 7 f (x) m 0:"? [0,2] 8. f (x) m on [2.4] x — 3 x «- 3 yW /W'erw/g wﬁéfgéw’a’ “‘9'?” L91} 1* 9“] “9W”! gfwntﬂeg'm Mg. £4 M/LﬁgWM/é? 52W 42(5); 3 m 273 ﬁg: 3"" "”5 Wlﬂaﬁda 53/2. ail/ace reawiéwiujém 4% 2.5 3 ~— .1 7:94?) (iﬁrgﬂugjﬂ’ir mf/‘V‘Lim;£d4§nww m “’ 3-1 ix.rg\€.xt.“/& WWW coil:- F‘ we}. fhmj, ”waxév ”WW/2W 4;» W 27% WM ...
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