A ball is thrown into the air with an initial upward velocity of 46 ft/s. it's height h in feet after t seconds is given by the function h=-16t squared plus 46t plus 6

Given the function

h = - 16t^2 + 46t + 6

and the initial velocity of 46 ft/s

to solve for the maximum height, first we must solve the time it reaches the maximum height. this done by getting the first derivative and equate it to zero

h = - 16t^2 + 46t + 6

dh/dt = - 32t + 46

-32t + 46 = 0

t = 1.4375 s it take to reach the maximum height

so the maximum height is

h = - 16t^2 + 46t + 6

h = - 16 (1.4375^2) + 46 (1.4375) + 6

h = 39.0625 ft