Derivative Practice Corner: Visualizing Derivatives Graphically

① This applet demonstrates the graphical interpretation of the derivative for any user‑defined function, showing how the tangent slope varies with the independent variable. ② Core mathematical concepts include the definition of the derivative, tangent lines, slope functions, and the geometric meaning of the derivative function. ③ Construction highlights: Textfield and InputBox for editable function input; Point to mark the variable point A; Tangent to draw the tangent at A; Slope to compute the tangent’s slope; Derivative to generate the derivative function f' and its graph g. Key objects are f, f', A, b, m, B, c, and several text labels. ④ Suitable for high‑school calculus introduction, undergraduate calculus review, and classroom demonstrations to build geometric intuition about derivatives.