A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght

For this case we have the following equation:
 h = -16t ^ 2 + 184t + 20
 Deriving we have:
 h '= -32t + 184
 We equal zero and clear t:
 -32t + 184 = 0
 32t = 184
 t = 184/32
 t = 5.75 s
 Then, the maximum height is given by:
 h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20
 h (5.75) = 549 feet
 Answer:
 It takes the boulder to reach its maximum height about:
 t = 5.75 s
 the boulder's maximum hieght is:
 h (5.75) = 549 feet