Another word problem involving the maximum or minimum of a quadratic function

Question

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function

What is the maximum height that the ball will reach? Do not round your answer.

Answer 1

Answer 2

h(t) = 72t - 16t^2

take the derivative and set equal to zero, then solve for t

h'(t)

= 72 -32t = 0

32t = 72

t = 72/32 = 9/4 = 2.25 seconds to reach max height

substitute that value of t, 9/4, into the original height equation to solve for max height

h(9/4) = 72(9/4) -16(9/4)^2

= 72(9/4) -16(9/4)(9/4)

= (9/4)[72 - 16(9)/4]

= (9/4)[72 - 36]

= (9/4)[36]

= 81 feet = maximum height

(that's not rounded off)