Final answer:
f(x) is positive in the interval (0, π/2) and (3π/2, 2), and it is negative in the interval (π/2, 3π/2). The function f(x) = sin(x) + cos(x) can be graphed in the interval 0 < x < 2. By analyzing the signs of sine and cosine in this interval, we can determine when f(x) is positive or negative.
Step-by-step explanation:
The function f(x) = sin(x) + cos(x) can be graphed in the interval 0 < x < 2 using trigonometric properties. To find the intervals where f(x) is positive or negative, we can analyze the signs of sine and cosine in the given interval.
In the interval 0 < x < 2, we can determine the signs of sine and cosine by analyzing their values at specific points. For example, at x = 0, sin(0) = 0 and cos(0) = 1, so f(0) = sin(0) + cos(0) = 1. This means that f(x) is positive at x = 0.
By analyzing similar points in the interval, we can determine the intervals where f(x) is positive or negative. In this case, f(x) is positive in the interval (0, π/2) and (3π/2, 2), and it is negative in the interval (π/2, 3π/2).