The minimum is going to be at x = π /3 . This is because since the domain is x>0, the minimum value for the smallest x will be at the bottom of the drop after f(0). The bottom of the drop would be found at this value.
(If you want a decimal value, it would be around 1.047)
The smallest positive value of x for which y = cos ( 3 x ) has a minimum value is 3 π . This occurs when 3 x = π .
;