Finding Derivative Using Curve Fitting

Draw a function curve and select multiple points on it. At each selected point, construct a tangent line to the curve, making sure the tangents are clearly visible and touch the curve exactly at those points. Then, based on the slopes of these tangents, create a set of points in the coordinate plane representing the derivative values. Fit a smooth curve through these derivative points using polynomial fitting of degrees one, two, and three, and choose the best-fitting curve to approximate the derivative function. The final graph should include the original curve, the tangent lines, and the fitted derivative curve, illustrating the geometric meaning of the derivative.