Answer:
h(t) = -4t² + 12t + 5
a. h'(t) = -8t + 12 = 0
8t = 12
t = 1.5 seconds
h(1.5) = 14 feet
b. 4t² - 12t - 5 = 0
t = (12 + √(12² - 4(4)(-5)))/(2×4)
= (12 + √(144 + 80))/8
= (12 + √224)/8
= (12 + 4√14)/8
= (3 + √14)/2 = about 3.37 seconds
The ball reaches the ground in about
3.37 seconds.