Question

1. Let g(t) = We are given g'(t) 2-3 31(12-9) (12 - 3)2 and "(t) 186(+9) (t2-3) (a) Determine the domain of g. (b) Determine the intervals of increase and decrease. Show your work, explaining using a sign chart or other explanation. Then state all possible relative maxima/minima. (c) Determine the intervals of concave up and concave down. Show your work, explaining using a sign chart or other explanation. Then state all possible inflection points.

Answer 1

ght) = x² t²3 0 @ To find domain of get) Denominator #0 - 3 0 =) t+18) (tr) to w Domain - R-f-8.8 © =0 14) >0 ght 29 gire) = = 3% (ta) (t²-3)2 a) t-o, t-73 we take intervals 600B) 16-3,0), (0,3) € (3,00) In the intervals (-00, 3) & 0,00) g'lt) ~ glu) is increasing In the interval (+ 3,3% is decreasing g"(t) = 18tt'+9) when t=on g"(t) = 0 (t2-3)3 t=43, gult) =48(3) (18) = 78 X 3X183 8x6x6 2 = =) df.530 when t=-3, gillt) =-4.520 7 At t=-3, git) has minimum value, ges) 9-3 gles 3x3 3x3 9893 62 = 27 minim un 13-5 * minimum =- 13.5

t: +3) git) = 3(427) 62 = 13.5 maximum = 13.5 © g"(t) = 18 41449) (t2-33 points gullt)=0, To find inflection os 18+ (479) =0 t=0, t=013 t-o is the inflection point 9"14) >0, » gilt) then get) is concave up in etue intervals 6-2013, (8,00) concave down in the interval (-3,0) is increasing