Find the maximum and the minimum values, if any, without using derivatives of the following functions: f (x) = sin 2x + 5 on R

Given $f(x)=\sin 2 x+5$ on $R$
We know that $-1 \leq \sin 2 x \leq 1$
$
\begin{array}{l}
\Rightarrow-1+5 \leq \sin 2 x+5 \leq 1+5 \\
\Rightarrow 4 \leq \sin 2 x+5 \leq 6
\end{array}
$
Hence, the maximum value and minimum value of f are 6 and 4 respectively.