Gradient of y=x²: Tangent Slope and Derivative Visualization

① This interactive GeoGebra example dynamically illustrates how the slope of the tangent line to the parabola y=x² changes as a point moves along the curve, while also showing the secant slope approaching the tangent slope. ② The core mathematical concept is the geometric meaning of the derivative: the derivative at a point equals the slope of the tangent line, involving limits, difference quotients (average rate of change), and tangent line equations. ③ Construction details: using GeoGebra commands Line, Tangent, and Slope, the applet builds the function f, a movable point P, a small increment δx, an auxiliary point Q, a secant line g, a tangent line h, and slope values m and m_1, allowing users to drag P or adjust δx to observe slope behavior. ④ Suitable for high school or introductory college calculus students to grasp the definition of the derivative, tangent slope, and instantaneous rate of change, and also useful for teachers as a classroom demonstration tool.