Calculator question: A particle moves along the x-axis so that at time t is greater than or equal to 0, its position is given by x(t)=(t+1)(t-3)^3. For what values of t is the velocity of the particle increasing? (A) all t (B) 03 Answer is E...please show work on how to get to this answer. Thank you

Question

Calculator question: A particle moves along the x-axis so that at time t is greater than or equal to 0, its position is given by x(t)=(t+1)(t-3)^3. For what values of t is the velocity of the particle increasing? 
(A) all t (B) 0<t<1 (C) 0<t<3 (D) 1<t<3
 (E) t<1 or t>3
Answer is E...please show work on how to get to this answer. Thank you

richyw · Answer

if the velocity of the particle is increasing, it means that the acceleration is positive. velocity is the time derivative of position x(t) and acceleration is the time derivative of velocity.