Part 2/6:
The graph of ( y = \sin x ) is a smooth, periodic wave that oscillates between -1 and 1. As we observe the graph, we note specific points where the slope of the sine function is zero. These points occur where the graph transitions from an upward movement to downward and vice versa—specifically at multiples of ( \pi ) (0, ±π, ±2π, etc.).
At these x-values, the derivative, or the slope of the sine function, equals zero. Additionally, when sine is at its maximum or minimum (i.e., 1 or -1), the derivative transitions to positive or negative values indicating the function's increase or decrease.