Tangent to Cubic: Open Middle Problem

① This interactive GeoGebra example presents an Open Middle Problem where students must find tangent lines to a cubic function under given constraints, exploring multiple valid solutions. ② Core mathematical concepts include the derivative as the slope of a tangent, tangent line equations, cubic functions, and optimization thinking when adjusting parameters to satisfy conditions. ③ Construction details: based on the summary, the applet uses text fields (Textfield, InputBox1/2/3/6/7), a button (button1), parameters (a, b, c, d, e, j), functions (f, g, h), points (A, p), and conditional logic with If and Length commands to validate inputs and dynamically update the graph. ④ Suitable for high school or introductory college calculus, this activity reinforces the geometric meaning of derivatives and encourages problem-solving and exploration in a digital environment.