Vertical Shifts and Derivatives

This example demonstrates the geometric relationship between vertical shifts of functions and their derivatives. When a function f(x) is shifted vertically by k units to obtain g(x)=f(x)+k, its derivative remains unchanged because the derivative of a constant is zero. Construction: ①Use InputBox for interactive parameter adjustment; ②Define original function f(x) and its derivative f'(x); ③Create shifted function h(x)=f(x)+m; ④Display function expressions via Textfield. Key GeoGebra objects: InputBox1/2/3, f/g/h functions, f' (derivative), Textfield. Ideal for high school calculus introduction, helping students intuitively understand the geometric meaning of derivatives and properties of function transformations.