Derivative of a Constant Function: Verifying Zero Slope in GeoGebra

This example demonstrates the key calculus fact that the derivative of a constant function is identically zero, visualized via the idea of slope of the tangent line. It focuses on the definition/geometric meaning of the derivative, the property of constant functions (no change with respect to the input), and the correspondence between tangent-line slope and the derivative value. In construction, the GeoGebra setup relies on Textfield to display explanatory text and computed results, alongside input text fields/objects (e.g., InputBox1 and function/text objects) to enter the constant and form the function expression, then present the derivative conclusion clearly (showing it as 0). Suitable for high-school calculus introduction and early university calculus lessons, especially for teaching and checking the “constant function → derivative equals zero” concept with a graph-based approach.