Aball is thrown into the air with an upward velocity of 48 ft/s. its height h in feet after t seconds is given by the function h = -16t^2 + 48t + 6. how long does it take the ball to reach its maximum height? what is the ball's maximum height?

So you have to find the velocity (or first derivative) from the position function of h=-16t^2+48t+6

the velocity is -32t+48 which you then have to set equal to 0 in order to find t
-32t+48=0
-32t=-48
t=1.5

you then take your t value and sub it back into your original position function
-16(1.5)^2+48(1.5)+6 which will give you a maximum height of 42 feet

so the time it takes is 1.5 seconds to reach a maximum height of 42 feet