Question
Find the maximum or minimum values, if any, of the following functions without using the derivatives:
|sin 4x + 3|
Solution
Let f(x) = |sin 4x + 3|
∵ – 1 ≤ sin 4x ≤ 1
∴ – 1 + 3 ≤ sin 4x + 3 ≤ 1 + 3
⇒ 2 < sin 4x + 3 ≤ 4 ⇒ 2 ≤ | sin 4x + 3 | ≤ 4
⇒ 2 ≤ f (x) ≤ 4
∴ maximum value of f (x) is 4 and minimum value of f (x) is 2.
