Atennis ball machine serves a ball vertically into the air from a a height of 2 feet, with an initial 110 feet per second. what is the maximum height, in feet, the ball will attain?

Thank you for posting your question here. I hope the answer below will help. 

Vo=110 feet per second 

h0=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 aka when h'(t)=0. 

So, set h'(t)=0 and solve for t: 

0 = 110 -32t 

-110 = -32t 

t=3.4375 

t=3.44 seconds 

first one because it can't have a fraction in it

step-by-step explanation: