The function h (t) = - 16t^2 + 16t represets the height (in feet) of a horse t seconds after it jumps during a steeplechase. At what time does the horse reach its maximum height in seconds (write as a decimal) ? seconds

Calculation of relative maxima and minima of a function f (x) in a range [a, b]:

We find the first derivative and calculate its roots.

We make the second derivative, and calculate the sign taken in it by the roots of the first derivative, and if:

f '' (a) <0 is a relative maximum

f '' (a) > 0 is a relative minimum

Therefore,

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

h ' (t) = - 32t + 16

-32t + 16 = 0

t = 16/32 = 1/2

h '' (t) = - 32

h '' (1/2) = - 32 (<0 is a relative maximum)

answer:

The horse reaches its maximum height in 0.5 seconds