The function s(t)= t^3/3-6t^2/2+5t+7 describes the position of a particle in motion. For what interval is the particle moving backwards?

Question

anonymous · Answer

in other words, for what interval is the velocity negative!

anonymous · Answer

yeah i know what it means dude... I just need to know how to get to the correct answer

anonymous · Answer

take the derivative, find the critical points.|dw:1364774510905:dw|

anonymous · Answer

you will get three intervals. check in what interval is the sign of the derivative negative!!!
and do not call me dude.

anonymous · Answer

this is so becasue the derivative of position is the velocity function.

anonymous · Answer

the derivative of the function is t^2-6t+5... i set it equal to 0 and got t=1 and t=5

anonymous · Answer

|dw:1364774761880:dw|
in each of those intervals, take a value for "t" and find the sign of the derivative.