Question

In this activity we practice the 8-step process for curve sketching from Stewart's Calculus book. A. Domain E. Intervals of increase or decrease B. Intercepts F. Local maximum and minimum values C. Symmetry G. Concavity and points of inflection D. Asymptotes H. Sketch the curve Follow the process, make your sketch, and only then use a graphing program to check your work.

Answer 1

lt t2 4.) (t) = A) Domain of w(H) is Since, t+1>o. Domain; te (-00, ao) *E(-ao, ao) y- Interupt, set too. ly=0 where y = Yu(t) t-interupt, set y=o + Itt² It=0 c) symetry, -t w(t) is symmetric about D) Assymtote of wilt) does not exist. 4 #70042 +1 lim *100 (4) با lim + A do 1+42 lim 17 oti lim H-00 Wit) - lim tot-on + Ht2 V I lim t 1 Hal OtI "4241 E) wilt) = (1+1²) - +2+ (1++292 = 0 1-t² = 0 =) t= Il

wiltlo ou (-1, 1) on (-1, 1) wilt)co w(t) increasing on (-00,-1) U (1, do) Wct) decreasing on (-00,-1) U (1, ao) F) W"(t) = 2+ (+²+1)²_ 2 (+²+1) 2+ ( +_+²) (+²+124 In order to find the inflection point set W"(t)=o. -24(+²+1[*+1-201-+2)] = 0 - 2000) (+2+124 -2+(+²+1) (2+²-1) .. t=0 and t=th at a t= -1 W"E) = 4)o : W(t), has local Minimal at tanl is = 2 at t=1 W"(1)=-4col Wit) has mamina at tal is 1 2

(G) WI(+)=0 & t=0 t = 7 are inflection points Wit) >0 on Colul,00) W(t) is concame upward on ( ) (Goo) WICH) <0 on (-20, - 1 1 0(0, 1/2) (-00, sau (0) W(t) is concame downward on Graph of w(t) =- g + +2+1
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