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 $[0,5]$ seconds. Recall that the speed of a parametric curve is given by s$($t$)=($x$\text{'}($t$))2+($y$\text{'}($t$))2.$

$($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