Sketch the Derivative of a Function
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Sketching Derivatives
This example demonstrates how to sketch the derivative of a given function based on its graph. Key mathematical concepts include derivatives and polynomial functions. By constructing objects such as function f, its derivative f', root a, point A, auxiliary function g, point B, auxiliary line h, and point b, students can understand the geometric meaning of derivatives. Suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
f(x) = (ln(abs(x)) * 3)f'(x) = f'(x)Numeric a(-7)(a, f(a))g(x) = If[a - 1 ≤ x ≤ a + 1, f(a) + (f'(a) * (x - a))](a, f'(a))f'(x)Boolean b(false)
AI Drawing Prompt Reference
Draw a geometric sketch showing a function and its derivative. Plot the main function f(x)=3·ln(|x|). Choose a numeric value a=-7 and mark the point (a, f(a)), as well as the corresponding derivative point (a, f'(a)). Define an auxiliary function g(x) that is used only on the interval a-1≤x≤a+1, where g(x)=f(a)+f'(a)(x-a), representing the local linear approximation governed by the derivative at a. Also display the graph of f'(x) in the same coordinate system, emphasizing that g(x) passes through (a,f(a)) and has slope determined by f'(a).
The prompt above was compiled from the original drawing commands and is for reference only.