pls help pre calc story question

Question

If a baseball is projected upward from ground level with an initial velocity of 128128 feet per second, then its height is a function of time, given by sequals=minus−16tsquared2plus+128128t.
What is the maximum height reached by the ball?

Answer 1

To find the maximum height obtained by the baseball, first find the derivative of the height function s(t)

 

s(t) = -16t² + 128128t

 

s'(t) = -32t + 128128

 

s'(t) is the derivative of the height function, and the maximum height will occur at one of the critical numbers, which is where s'(t) is either undefined or equal to zero. The function s'(t) is defined for all real numbers, so we only need to set s'(t) equal to 0 and solve for t.

 

Once you obtain that critical number (in this case there is only one), you may plug it back into s(t) to determine the maximum height, Ses.