How to calculate the minimum and the maximum value of the function f(x) = 3 cos3x - 4 sin3x - 2 ?

Find the derivative of the function, and then set the derivative to zero, solving for x.

Or if you can do a sketch of the curve, you can already state the maximum and minimum values.

Do you know how to do that?

Well, not really.

I haven't learnt about derivatives yet, so I guess the curve will help more.

In this case, I can deal with it, I just didn't know this exercise required some other knowledge.

Thank you very much.

Derivative is just the same as differentiation, okay :)

Otherwise, to make drawing easier, you could change it like that

\cos (3x) - \sin (3x) = R \sin(A-\alpha)

If you know how to use that.

Expand the right:
\sin(A-B) = \sin A\cos B - \cos A \sin B

Then, put B = 3x
If you can understand what you're doing, I'm sure the graph will become easy. :)