The Derivative of f(x) = lnx
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This example demonstrates how to use GeoGebra to plot the graph of the natural logarithm function f(x) = lnx and its tangent line at any point a. Core mathematical concepts include the geometric meaning of the derivative (slope of the tangent) and the local properties of function graphs. Construction highlights involve using the Tangent command to draw the tangent line, the Slope command to calculate the slope, and the interactive definition of objects f, a, P, g, b, h, m, P', text1, c, d, text2. Suitable for high school and above students to understand the relationship between derivatives and function graphs, and to master basic GeoGebra drawing techniques.
GeoGebra Commands & Parameters
Tangent(P, f) → hSlope(h) → m
AI Drawing Prompt Reference
Plot the graph of the natural logarithm function and show its tangent line at any point on the curve, while labeling the slope of the tangent to demonstrate the geometric meaning of the derivative and the local properties of the function graph. First, draw the curve of the natural logarithm function, then select a point on the curve to draw a tangent line through it, calculate the slope of the tangent line, and finally label the tangent and its slope on the graph.
The prompt above was compiled from the original drawing commands and is for reference only.