Trying to find the right answer to this..

Application of Derivatives

Question

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
sin (sin x)

Answer

Let f (x) = sin (sin x)
For any x, – 1 ≤ sin x ≤ 1
⇒ sin (– 1) ≤ sin x ≤ sin 1 {∵ in [– 1, 1] , sin function is increasing}
⇒ – sin 1 ≤ f (x) ≤ sin 1
∴ maximum value of f (x) is sin 1 and minimum value of f (x) is – sin 1.