Question

Consider an object moving along the parametrized curve with equations: x(t)=et + e–t, y(t)=e–t where t is in the time interval [0,7] seconds.

(a) The maximum speed of the object on the time interval is ___ at time ___.

(b) The minimum speed of the object on the time interval is ___ at time ___

Answer 1

solution alt=ettet Interval Co,?] yetl=et het "v le the speed we will maximize /& minimize av alt= ettet l ylH=et de luz et- ét I dyte et v letech 14 ) = (est) 764)2 ve et texte text v et at dezt a To find max of min speed to find critical points

(etxetx) =0 ezt a tzezt (-2) -0 =0 zezt_4e2t zo zezt = 4 ezt et = 42 جدید به اتے est az Inlett)= lnia) ata lucas t = 2 luniz) To check whether we have max & min speed at the critical point t= + Inca) CPV = ( *4224) a ze tips teken 1 = 4 ett gezt t=212) = 482 +8 (4) = 482 +4f2=852

Double derivative of v is so f 1 102) >0 At taflna we have to the minimum speed We also check at. Intuvad Extremetics v=det +2e24-2 = At v=Jetze -2 t=0 √ 1+2/-z r =1 At t=7 »v=J ettze 14-2 B - 1202 604.284 +1663057436X102 = 1096.63 2246 ~ 1096.6 of t=2 luz a v=52121m2) 2 2212 luz) v=5z + 2 (72) - 2 v= 552 +82-2 = 0.91017921 A => E0 = v= ! At a t=7 va 1096.6 At > t = £ ln(2) > V ~ 0.9102 = max speed → min speed