Consider $f(x)=\sin(3x) + 4, ∀ x ∈ R$, Then

(A) Maximum value of f(x) is 5
(B) Minimum value of f(x) is 3
(C) Maximum value of f(x) is attained at $x=\frac{π}{6}$
(D) Minimum value of f(x) is attained at $x = 0$

Choose the correct answer from the options given below:

(A), (B) and (C) only

The correct answer is Option (1) → (A), (B) and (C) only

(A) Maximum value of f(x) is 5
(B) Minimum value of f(x) is 3
(C) Maximum value of f(x) is attained at $x=\frac{π}{6}$

Given function: f(x) = sin(3x) + 4

Maximum value of sin(3x) = 1 ⇒ Maximum of f(x) = 1 + 4 = 5

Minimum value of sin(3x) = -1 ⇒ Minimum of f(x) = -1 + 4 = 3

sin(3x) = 1 ⇒ 3x = π/2 + 2nπ ⇒ x = π/6 + 2nπ/3

sin(3x) = -1 ⇒ 3x = 3π/2 + 2nπ ⇒ x = π/2 + 2nπ/3

Check options:

(A) Maximum value of f(x) is 5 → Correct

(B) Minimum value of f(x) is 3 → Correct

(C) Maximum value attained at x = π/6 → Correct (for n=0)

(D) Minimum value attained at x=0 → Incorrect (f(0) = sin0 + 4 = 4 ≠ 3)