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HW_sol(10) - Sections 4.3(Due Thursday 10/25 Descrigtion...

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Unformatted text preview: Sections 4.3 (Due: Thursday, 10/25) Descrigtion: This homework will help you learn: - the use of the first derivative to determine whether a function is increasing or decreasing, - the First and Second Derivative Tests for local maxima and minima, - the use of second derivative to determine concavity and points of reflection, - the geometric description of concavity, and the relationship between concavity and the behavior of the first derivative. ' Show all work to a A II credit. 1) Use the given 0 find the following. Domain'. (0) 6) (a? The open intervals on which fis increasing. ( oi WW, (bLThe Q99 [lifllfii‘filS 0“ mieflllié C19£E§§§lfl© ‘ ‘ , i .. Ll ;) (cflThe og‘en interval on which fis concave upward. ! ~ M (cnghe ogen intenlalon which f‘j‘smcongaveggwnward. ( , \\m“umm }\mwu\\j ‘w.“ \A\\\ S“ .... ...... ....... 4,1)o(§ ..................... i ................... .i) ‘ h ' f h g ' 1 f'nflectign. ‘ni wl‘m * 1‘3 c» i ‘ e fillimfiflégglgjégéfit e om o l w Pm fir glazes, tutu/:42? 2) (a) On what intervals is f increasing “me \ §“\\\mmm\nv~\\\nj \““\\W\\\\\\\\\ §xs~\\\\\\wmmmva (i O ,3 1 3)o({.3>....3,§ (b ‘On whatmingervalsis f decreasing? (in ‘ 4 , l ,3) ,,.)o({‘m'5 ..... )6 ) - (0) At what values of xdoes fhave a local maximum or minimu . \ {W A 3 =§ i.itVVA,.....,Hé(smallest value) ‘OLQL max VOL 3: 0 Ma ::::;‘\;‘g‘;?§(largest value) [@0945 mm 3 tau—l: i lnas lac-a9. Max it x: ,L anol‘)x:5 WW, w «90ml. twin a‘l’ X: 2.) U r Student Nam 3) The rah of the second derivative " of a function fis shown. State the X-coordinates of the inflection points of f. W =; 3.. 3(smallervalue) x . WNW. x :(Iargervalue) 4) Consider the equation below. (If you need to use —oo or oo, enter -|NF|N|TY or INFINITY.) f(x)=2x3+3x2-180X 0mm 34-00,”) a“): sz 4, 6K_\20 (gi‘ngmtflhe iiritervaisgon wiich fis‘ivngcrwemasuiflg; = “XI + X - a (b‘l‘firlgmtuhe intervalmon which fis decreasing. ) = Q (X + G’) (’< ‘5 -b’fi) £00 -.- c a xz-G or x=5— go) Find the loca minimum and maxirnum valueiof f. ‘ X '0“ a [3 5” 00 £6 — 5% 5mm) its): 1536.5 1. no.2, w + ewe? if“: a-<*r+3-<*>"‘*°(~‘>.® N (d in t ein ectign point. 3 a 1 . (is 0.5., 60,5 ..) il- 3:10.94 SH)— ” 4) (elflme [Interymafllfign which fis concave up. a a?“ X) : A 9- X + x6 .1 ($-05; co ) 31:00.4) ,) A2x+6=0=)x:—2 (I Find the interval on which fis concave down. 4 fwww W‘M‘W"; >< -90 — L 00 (‘ 7’( ' (9) Use this informatio to sket h the graph. X (5ce m Par} Judged :ll ) I V 5) Find the v | e of fusing b‘ t the First Deriv tive Testst—Jf'” , > 1‘5/ 3m): Mai—x3 A)» II x/0 I‘( , c1 :1 iii; em to + N5 ow => cant: I V =0 . A:.L—— w I,» gust“) 4’[ 6) Fin the critical n mbers of the function and describe thgbéhawor of fat the enur—nbers. (List . our answers in increa in 0rd ,1 tr: ' 1. EmeUf/(xhfix-I‘ Ex:o x:l x3 )(ahx)': (3:; mx _ I I g ‘=) HUI—x): 7) Suppose 1'" IS tinuous on (-00, oo). ‘ a Ig_ L“: I _ (a) If “4) = o and M4) = “6, what can you say about i”? _> A 5 - HX -A = z a - — ix 1* 7‘? => 4.5. = x I MO SNE act x:l-I,. (find Oré‘t’fcci 0.2.) X-V0»‘NLQ as, COR 1.’ 41K) :0 .1) Exhflx-0h Axbxx-DS; O —+~,’*\~9 fihfifQé—D + 1+x1=0 f Gaul: 409% =3 x30 X=L \ 5(xf‘)+hx :0 . Condom-W , W~‘ ) ————-—"'—'- gm ’60 As aplng =9 5x -5 4 um; 5m+acwis= a £00 21$ 04 NM~ =9 9x-5=-O X'JO "3 W3 Pn'vds “‘15 can» $3 x 2 X:. x = 5/3 Student Name: I x = 4 is a local maximum of f. g: x: 4 is a local minimum of f. ["2 x: 4 is not a maximum or minimum of f. There is not enough information. If f' 5 = O and f" 5 =0, what can ou sa about f? ) ( ) ( ) \“K Y a+ x:5- > be in (3 about Duncan/lg, x: 5 is a local maximum off. HEEL”? x: 5 is a local minimum off. L"? x: 5 is not a maximum or minimum off. There is not enough information. ’ls umcLuiCll K=5 is 9.301 mm or max. 8) Let f(t) be the temperature at time twhere you live and suppose that at time t: 3 you feel uncomfortably hot. What happens to the temperature in each case? wwwwrwe rem—arr mew—6:57“) The temperature is increasing, and the rate of increase is increasing. , x L The temperature is increasing, but the rate of increase is decreasing. i. The temperature is decreasing, but the rate of increase is increasing. (039 E: v The temperature is decreasing, and the rate of increase is decreasing. ). , 3< <b>f'(3)=r,2“'<3>=—1 £‘Cb)>o a. tl‘ , ar”(5)<o at 5‘ L The temperature is increasing, and the rate of increase IS increasing. The temperature is increasing, but the rate of increase is decreasing. FEE The temperature is decreasing, but the rate of increase is increasing. if”? The temperature is decreasing, and the rate of increase is decreasing. item—uh: . Masha-91W E The temperature is increasing, and the rate of increase is increasing. E: The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of increase is increasing. E The temperature is decriasing, and the rate of increase is decreasing. (g>f'<3)=—1,f"(3)=—1 ’(5)<o .93\ , “aways E The temperature is increasing, and the rate of increase is increasing. E The temperature is increasing, but the rate of increase is decreasing. E The temperature is decreasing, but the rate of increase is increasing. i The temperature is decreasing, and the rate of increase is de reasing. Damaia (—96 ,os 9) Find the inflection point of the function below. . 999.:stximmwmmw ><>o : (x) -. 6x. x : 6x2. (Lam lxl = x, m) ,3. O 3) 4 37(X): nzx 93.n(X): ><<O : %(x): Qx(—x) : _ sz (hemp. lxlz-Kfrag —9 2:00 : Alba tom—AL :3 114‘th 1m Pant”; X:C) L 3(a): 07,77 ...
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