Given $f(x)=|\sin 4 x+3|$ on $R$
We know that $-1 \leq \sin 4 x \leq 1$
$
\begin{array}{l}
\Rightarrow 2 \leq \sin 4 x+3 \leq 4 \\
\Rightarrow 2 \leq|\sin 4 x+3| \leq 4
\end{array}
$
Hence, the maximum value and minimum value of f are 4 and 2 respectively.
Find the maximum and the minimum values, if any, without using derivatives of the following functions: f (x) = |sin 4x + 3| on R
Find the maximum and the minimum values, if any, without using derivatives of the following functions: f (x) = |sin 4x + 3| on R