If the derivative f'(x) of the function f(x) is greater than or equal to 0, then f(x) monotonically increases at x.

Therefore, if the series {a(n)} has the recurrence relation a(n+ 1)=f(a(n)) and the derivative f'(x) of the function f(x) is greater than or equal to 0, the series {a(n)} must increase monotonically.

Similarly, if the derivative f'(x) of the function f(x) is less than or equal to 0, then f(x) monotonically decreases at x.

Therefore, if the series {a(n)} has the recurrence relation a(n+ 1)=f(a(n)) and the derivative f'(x) of the function f(x) is less than or equal to 0, the series {a(n)} must be monotonically decreasing.

For the sequence {a(n)}, each item a(n) in it

) is the value of the independent variable x of the function f(x). Therefore, when f'(x) is greater than or equal to 0, for any x 1 and x2 (where x 1

So, if the series {a(n)} is a decreasing series.

(a( 1)>=a(2)), even if f'(x) is still >; =0, the sequence {a(n)} will not increase monotonically, but decrease monotonically.

This is because the monotonicity of the sequence {a(n)} depends on the monotonicity of the recurrence relation a(n+ 1)=f(a(n)) and the function f(x), but not on the initial value of the sequence {a(n)}. Therefore, even if the initial value of the sequence {a(n)} is decreasing, as long as the derivative f'(x) of the function f(x) is less than or equal to 0, the sequence {a(n)} will still decrease monotonically.

Therefore, the conclusion is correct.