# Find the maximum and the minimum values, if any, without using derivatives of the following functions:f(x) = |sin 4x + 3| on R

We know that – 1 ≤ sin4x ≤ 1

= 2 ≤ sin4x + 3 ≤ 4

= 2 ≤ |sin 4x + 3| ≤ 4

Hence, the maximum and minimum value of f are 4 and 2 respectively.

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