I have a question in math

Question

NASA launches a rocket at t=0t=0 seconds. Suppose its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+82t+381h(t)=-4.9t2+82t+381.

How high above sea-level does the rocket get at its peak? Round your answer to 2 decimal places.

The rocket peaks at  meters above sea-level. 

Answer 1

h'(t) = -9.8t +82 =0

t = 82/9.8 = 41/4.9 = 410/49 = about 8.37 seconds to reach maximum height

max height = h(410/49) = -4.9(410/49)^2 + 82(410/49) + 381

= (410/49)(-4.9(410/49) + 82) + 381

= (410/49)(-2009/49+ 82(49)/49) +381

= (410/49)(2747/49)+381

=-1126270/2401 + 381

= 2041051/2401

= 850.08 meters = maximum height