Answer to Question #324936 in Calculus for Joyboy

Question

Let (fn) be defined by ∀n ∈ N

f : [0,π/2] → R

x → n(cos(x)^n)(sin(x))

1. Show that f has at most one maximum value at a point xn. (xn is a maximum point of fn(x))

2. Show that xn ∼√n