Question

What is the maximum value of the function `y=2sin3x`?

Answer 1

The max value of function `y = 2 sin 3 x` is 2.

Explanation:

We can probe it using derivatives, but it's more easy to think about proporties of function `f (x) = sin x`.

All we know that kind of function has a periodic change between values `- 1` and `1`. Then, changes in the argument of the function as the substitute `x` by `3 x` modify the period of the latter but not its extreme values, which remain `- 1` and `1`.

When multiplying the function by the coefficient `2`, what we do is multiply its values by `2`, so that the function changes from `- 2` to `2`, and its maximum value will be the latter.