Question

A body moves along a horizontal line according to s=f(t)=t^3-9t^2+24t a) when is s increasing and when it is decreasing? b) when v is increasing and when it is decreasing?

Answer 1

We know v(t) = f'(t)

Find the range of values for which v(t) is positive, these correspond to the points in time which the body is increasing (in position).
Likewise, the values for which v(t) is negative correspond to the point in time in which the body is decreasing (in position.

Knowing a(t) = v'(t) = f''(t), determine the point in time such that a(t) is positive. This corresponds to when the velocity is increasing. Similarly, whenever a(t) is negative, velocity is decreasing.