Specify the intervals of increasing function y = 1/2 Cos 3x + 1/2

We have a function:

y = 1/2 * cos 3x + 1/2.

Ascending interval of a function – an interval of a function, in which a larger value of an argument corresponds to a larger value of a function.

Let’s find the derivative of the function:

y ‘= 1/2 * 3 * (-sin 3x) = -3/2 * sin 3x;

The function increases where its derivative is positive, which means:

-3/2 * sin 3x> 0;

sin 3 x <0;

The sine value is negative in 3 and 4 coordinate quarters, which means:

P + 2 * P * N <3x <2 * P + 2 * P * N, where N is an integer.

P / 3 + 2/3 * P * N <x <2/3 * P + 2/3 * P * N, where N is an integer.