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)
 
 The horse reaches its maximum height in 0.5 seconds

Okay i already have it though