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.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right