Differentiability vs Continuity
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This example illustrates the relationship between differentiability and continuity. It demonstrates the difference between a function being continuous and differentiable through specific functions. Users can observe cases where a function is continuous but not differentiable. The core mathematical concepts involved are the continuity and differentiability of functions. The example uses GeoGebra objects a and b, and function f. It is suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
Numeric a(-2.1)Numeric b(7.6)f(x) = If[x < 2, x^(2) - (2 * x) + 3, (a * x^(2)) + (6 * x) + b]
AI Drawing Prompt Reference
Draw a function that is x^2 - 2x + 3 when x < 2, and ax^2 + 6x + b when x >= 2. Adjust parameters a and b to observe continuity and differentiability at x=2.
The prompt above was compiled from the original drawing commands and is for reference only.