Find the absolute minimum and absolute maximum values of f on the given interval.

Question

f(t) = 8 cos t + 4 sin 2t,
[0, π/2]

Answer 1

f ' (t) = -8sin t + 2(4 cos t)
= -8sint + 8cost
= 0 for a max/min

8sint = 8cost
sint/cost = 1
tant = 1
t = 45° or 225° or t = π/4 , t = 5π/4 -->(outside our domain)

so evaluate
f(0)
f(π/4)
f(π/2)
and determine which is the largest and which is the smallest

Answer 2

Let g(s)=s^2+4 and h(s)=√(s^2-4).
Describe the domain of h(s).
Find h(g(s)), simplify your answer.