Question

how do I find the minum value of the function f(x)=-11 cos(3x)-3?

Answer 1

"minimum value," right?

Answer 2

Actually, your function has many minimum values (all the same number).det
Why not determine 2 or 3 of the minimum values that are closest to x=0?

Answer 3

Looking at the given function, I see that f(x) reaches its smallest possible value, -11-3, when cos 3x = +1. It is certainly possible for cos 3x to = +1.

This question does not say you have to find the x-coordinate(s) of the minimum(s). If you need to or want to do that, find the zeros of cos 3x.