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:
Answer & explanation
Correct answer: option 1
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)