A particle moves a long the xaxis such that t is given by st

A particle moves a long the x-axis such that t is given by s(t): t^3 - 6t^2 + 9t + 11 feet During what time intervals is the particle moving left? Justify your answer.

Solution

Time period of moving left is given by the time intervals when the particle was moving with negative velocity

=> s(t) = t³ - 6t² + 9t + 11

=> s\'(t) = 3t² - 12t + 9

Finding s\'(t) < 0

=> 3t² - 12t + 9 < 0

=> ( t - 1 ) ( t - 3 ) < 0

=> t ( 1 , 3 )