If you differentiate again to get the maximum and minimum you get . So if you put in t=3, then 6t-2 is positive, therefore it is a minimum. If you put in t =-7/3 then 6t-2 is negative, so that is a maximum.
Oh right, I didn't see that it said 0<t<5. In that case the smallest possible value you can get in that range is t=0.