Examining the Derivative as the Slope of a Curve's Tangent

This example demonstrates how to dynamically show the derivative of a function at a point is the slope of the tangent line at that point using GeoGebra. Core math concepts include derivative, tangent function, polynomial functions, difference and slope, right triangles, and hyperbola. Construction highlights the use of Textfield command to display objects like function f, point P(x_p, y_p), slope m, intercept b, tangent t, function graph, x position, derivative f', text function, derivative text, textX_p, and textDerivative. Suitable for high school and above students learning calculus and analytical geometry.