A fountain shoots water from a nozzle at its base The height

A fountain shoots water from a nozzle at its base. The height h, in feet, of the water above the ground t seconds after it leaves the nozzle is given by

h(t) = 16t² + 14t + 8.

What is the maximum height of the water? Round to the nearest tenth.
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Solution

h(t) = -16t^2 + 14t + 8

For maximum height, dh/dt = 0

dh/dt = -32t + 14 = 0

t = 7/16 = 0.44 feet