Aparticle moves along the x-axis so that at time t its position is given by s(t) = (t + 1)(t - 3)3, t > 0. /p> for what values of t is the velocity of the particle increasing? (2 points) a.) t > 3 b. )1 < t < 3 c.) 0 < t < 1 and t > 3 d.) t > 0

Given the position function, the velocity function is obtained by taking the derivative:

The velocity is increasing its own derivative is positive, so we also have to find the acceleration by taking another derivative:

To find when , we first need to know where :

The quadratic factor is always positive (its discriminant is negative), which leaves one solution at . To either side of , we have, for instance,

which indicates that is increasing for , making the answer A.