Exploring Monotonicity Intervals of a Function

① This interactive GeoGebra example demonstrates how to determine the monotonicity (increasing or decreasing) intervals of a function on a given domain, visually highlighting where the function rises or falls. ② The core mathematical concept is the relationship between the derivative and monotonicity: the function is increasing where its derivative is positive and decreasing where the derivative is negative, with sign changes marking interval boundaries. ③ Construction details: The example uses a Textfield and InputBox1 for entering the function expression, defines the function f and its derivative g, employs a button (button1) to trigger calculations, a slider m to adjust the interval, and text objects text1 and text2 to display results. Points A and B are used to mark key locations on the graph. ④ This resource is suitable for high school or early college calculus students, serving as a visual aid for classroom instruction or self-study, and can be adapted by teachers to create interactive exercises on derivative-based monotonicity analysis.