Tangent Gradient to Sketch the Derivative

This example demonstrates how to sketch the derivative of a function by analyzing the gradient of tangents. ① It illustrates the geometric meaning of derivatives by dynamically adjusting tangent lines to observe the rate of change of the function at various points. ② Key mathematical concepts involved include the derivative, tangent slope, and function graphs. ③ Construction highlights the use of GeoGebra commands like Tangent and Slope, along with objects such as a, b, c, d, f_1, f, A, e, m, B, text1, text2, text3, Show, C, D, pic1. ④ Suitable for high school mathematics education, helping students understand the relationship between derivatives and the original function's graph.