Question

Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = sin(x) − 5 0 < x < 2

Answer 1

The function f(x) = sin(x) - 5 is increasing in the interval (0, π) and decreasing in the interval (π, 2π).

Step-by-step explanation:

The function f(x) = sin(x) - 5 is a combination of the sine function and the constant function. To determine on which open intervals the function is increasing or decreasing, we need to find where the derivative of the function is positive or negative. The derivative of f(x) is f'(x) = cos(x).

When cos(x) is positive, f(x) is increasing, and when cos(x) is negative, f(x) is decreasing. The cosine function is positive in the first and fourth quadrants (where x is between 0 and 2π or 0 and 360 degrees), so the function f(x) is increasing in the interval (0, π) and decreasing in the interval (π, 2π).