At what time of this position function does the particle reach it's maximum positive x position

x = 3t^2-2t^3

x is in meters and t is in seconds

thanks

this will occur when dx/dt =0

dx/dt = 6t - 6t^2 = 6t(1-t)=0

this occurs when t=0 or t=1

do the second derivative test:

d^2x/dt^2 = 6-12t

when t=0, >0 implies a minimum
when t=1 <0 implies a max...

therefore the greatest displacement occurs at t=1 s