What does "$\min\limits_x - \cos x$" mean in this optimization question?

Question

I have an assignment with different methods of optimization for the following:

Consider optimization problem $$\min_x -\cos x$$

I feel dumb but does this mean to use "$\cos x$"? What does $\min\limits_x$ mean?

Answer 1

$\min_\limits{x}f(x)$ means "find the minimum value of $f(x)$ over all possible values of $x$"

$\cos x$ is the trigonometric cosine function, and $-\cos x$ is the same function, multiplied by $-1$.

So the question is asking "what is the smallest value that $-\cos x$ can take?" which is the same as asking "find the largest value $\cos x$ can take, and multiply that by $-1$".