Differentiate and equate to zero

Hence

h'(t) = -32t + 14 = 0

32t = `4

t = 14/32

t = 7/16 Is the time to reach max. height

Hence

h(7/16) = -16(7/16)^2 + 14(7/16)

h(7/16) = -49/16 + 6 1/8

h(7/16) = 3 1/16 = 3.0625 = 3.063 (nearest thousandth).

h (t) = - 16 t² + 14 t

h ` (t) = - 32 t + 14 = 0 for turning point.

t = 14 / 32 = 7 / 16

h (7/16) = -16 [ 49/256 ] + 98/16

h (7/16) = - 49/16 + 98/16 = 49/16

Max height = 3•0625