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?

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?

richyw · Answer

$$\frac{ds}{dt} = 3t^2-18t+24$$$$\frac{d^2s}{dt^2} = 6t-18$$
a) when $\frac{ds}{dt}>0$, s is increasing, when $\frac{ds}{dt}<0$, s is decreasing

b) when $\frac{d^2s}{dt^2}>0$, v is increasing, when $\frac{d^2s}{dt^2}>0$, v is decreasing

richyw · Answer

oops the last statement in b should have a < sign (just like in a)