Derivative of |x|
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This example demonstrates the derivative of the absolute value function |x|. The key mathematical concepts involve differentiation of piecewise functions. Construction uses NDerivative command and objects f, g, a, A, B, h. Suitable for high school students learning calculus fundamentals or for function graph analysis practice.
GeoGebra Commands & Parameters
NDerivative(f) → g
AI Drawing Prompt Reference
Draw a coordinate plane showing the graph of the absolute value function y=|x|, which is a V-shaped polyline symmetric about the y-axis, with negative slope on the left and positive slope on the right. Also plot the derivative of this function as a separate curve: it is constant at -1 for x<0 and constant at 1 for x>0, with a discontinuity at x=0. Use different colors or line styles for the two graphs, and mark key points such as the corner at the origin and the jump in the derivative at x=0. The layout should be clear for comparing the function and its derivative.
The prompt above was compiled from the original drawing commands and is for reference only.