Question

What is the minimum value for y= 3cosx?

Answer 1

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