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

Question

Mathematics

Genevieve Ho

12 January, 21:00

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

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Ghoulie · 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
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.