Definition of Derivative - Task 1

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2020-07-19 02:27

Function Calculus Derivative

In collections Exploring Derivative

This example illustrates the definition of a derivative by dynamically adjusting the function and variable. Key mathematical concepts include functions, derivatives, and limits. It uses commands like Textfield, If, Tangent, Line, and Polygon in GeoGebra. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

Textfield(f) → InputBox1
Textfield(a) → InputBox2
If(d, (h, f(h)), (a, f(a))) → A
Tangent(A, f) → g
Line(A, B) → i
Polygon(A, H, B) → t1, b_1, a_1, h_1

AI Drawing Prompt Reference

Draw a function with a dynamically adjustable variable to illustrate the definition of a derivative. First, input the function and variable point, then plot the function value point based on a condition, draw the tangent line at that point, connect the tangent point and function value point to form a line segment, and finally fill the area between the line segment and part of the tangent line to dynamically show the geometric meaning of the derivative.

The prompt above was compiled from the original drawing commands and is for reference only.