Calculus Rates of Change Application

the function that represents acceleration is

h''(t)

the function that represents velocity

h'(t)

the object is slowing down when

h'(t) and h''(t) have different signs

The object is speeding up when

h'(t) and h''(t) have same sign

To find when an object is moving backward/downward, find intervals where

h'(t)<0

To find when the maximum height is achieved, we should

h'(t)=0 then plug into h(x)

To find when an object is moving forward/upward, find intervals where

h'(t)>0

To find the impact time we should

h(t)=0

To find the impact velocity we should

h(t)=0 then plug into H'(x)

To find when an object is stationary, look for points where

T=0