Tangent and Normal Line Equations

① This GeoGebra example dynamically demonstrates the tangent line and normal line equations at a point on a function curve, allowing users to drag a point or input an x-coordinate to see the lines update in real time. ② Core mathematical concepts include the geometric meaning of the derivative (slope of tangent), the normal line slope being the negative reciprocal of the tangent slope, the point-slope form of a line, and the relationship between a function graph and its lines. ③ Construction highlights: a Textfield and InputBox1 are used to input the x-coordinate x_t; the Tangent command generates the tangent line tanline; the normal line normline is constructed; checkboxes chkShowTangent and chkShowNormal control visibility; text objects txtTangent and txtNormal display the equations; point T marks the tangency point. ④ Suitable for high school or early college students learning calculus, this example helps visualize derivatives and line equations, and serves as a classroom demonstration or self-study tool.