Question

On which of the following intervals is the function f(x) = 4 cos(2x − π) decreasing? x = pi over 2 to x = π x = 0 to x = pi over 2 x = pi over 2 to x = 3 pi over 2 x = π to x = 3 pi over 2

Answer 1

The function is periodic, so it decreases and increases continuously at different intervals.
 From the intervals shown in the question, the function decreases in the interval from x = π / 2 to x = π.
 That is, π / 2 <x <π.
 If, for example, we replace a value within this interval in the function and then replace a new value greater than the first, we can see that the value of f decreases.
 If we substitute x = 2, then f = 2,615.
 Then we substitute x = 2.2 and we have for this case that f = 1,229.
 Finally 2,615 <1,229. This shows that in this interval the function is decreasing as x increases.
 Below is a graph of the function f (x) = 4cos (2x-π) for the mentioned interval.