What is the maximum value of $f(x) = 2\sin 3x + 5$?

Explanation

1. 01

   $\sin 3x$ lies between $-1$ and 1, whatever the 3 inside, so $2\sin 3x$ lies between $-2$ and 2.

2. 02

   So $f$ lies between 3 and 7, and its maximum value is 7.