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.

for what values of t is the velocity of the particle increasing?

B) an efficient process

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .