Visualizing Derivatives of Power Functions: Tangent Approximation to a Rule

This example demonstrates how the derivative of a power function can be visualized using a geometric/tangent-approximation setup, emphasizing the idea of turning an increment-based difference behavior into an instantaneous slope (limit intuition). It centers on calculus concepts such as derivative as a local rate of change, the derivative definition mindset, and the power rule for f(x)=x^n, along with parameter-driven arithmetic operations. The construction uses GeoGebra’s LaTeX command for mathematical labels and a set of constructed objects and parameters (a, h, k, b, n, g, f, and multiple text objects like text1/text2/text3/text4) to build the relevant points and show the geometric relationship behind the tangent/approximation. It is suitable for upper secondary to early university calculus, supporting teaching, explanation, and interactive exploration of derivative behavior for different exponents.