What is the minimum value for y = 3cosx?

Take the deritive

y'=-3sinx

find whre it equals 0

it equals 0 at - pi, 0, pi, etc

find whre it changes from negative to positive

at - 0.5pi, the derivitive is positive

at 0.5pi, the deritivie is negative

changes from positive to negative at x=0

that means that the max values are at pi and - pi in 2pi intervals

-pi, pi, 3pi, 5pi, etc

the min y value is - 3

so the minimum (s) are/is at (2aπ,-3) where 'a' is an integer