college algebra velocity

Question

A ball is thrown upward with an initial velocity of 64ft/sec from a height of eight feet. The function; s(t)=-16^2+64t+8 ;gives the height of the ball t seconds after release. 

Determine the time when the ball is at maximum height, and find that height. 

Answer 1

To find the time t when the ball is at maximum height, take the derivative of s(t) and find the critical numbers. The critical numbers will occur where s'(t) = 0. Since s(t) is defined and continuous for all real t, you do not need to worry about where s'(t) does not exist. Once you have the critical numbers, you can use the First Derivative Test to determine whether they represent a maximum or a minimum. You could also find the second derivative of s(t) and try to use the Second Derivative Test to determine whether they represent a maximum or minimum. The Second Derivative Test determines concavity.