Q. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height?

Explanation by: Chandani

It is launched vertically with an initial speed of 110 ft/sec.
It will reach maximum height when the speed drops to 0.
Vo=110 feet per second 
ho=2 feet 
So, h(t) = -16t^2 +110t +2 
Take the derivative: h'(t) = 110 -32t 
The maximum height will be at the inflection when the derivative crosses the x-axis, then h'(t)=0. 
So, set h'(t)=0 and solve for t: 
0 = 110 -32t 
-110 = -32t 
t=3.4375 
t=3.44 seconds.