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
