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Derivative Graphing Example by Laura Kinnel (4)

Derivative Graphing Example by Laura Kinnel (4)
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2020-09-21 05:18
FunctionCalculusDerivative
In collections Sketching Derivatives
This example demonstrates how to sketch the derivative of a given function. The key mathematical concepts involve the geometric meaning of the derivative and slope calculation. Construction involves GeoGebra commands such as f, f', a, A, etc. Suitable for high school students or college undergraduates to understand the relationship between the derivative and the original function.

GeoGebra Commands & Parameters

  1. f(x) = (2 * abs(x - 1)) - 4
  2. f'(x) = f'(x)
  3. Numeric a(-7)
  4. (a, f(a))
  5. g(x) = If[a - 1 ≤ x ≤ a + 1, f(a) + (f'(a) * (x - a))]
  6. (a, f'(a))
  7. f'(x)
  8. Boolean b(false)
  9. Point C(1, -2)
  10. Point D(1, 2)
  11. Point E(1, 2)
  12. Point F(1, -2)

AI Drawing Prompt Reference

In a single coordinate plane, plot the function f(x)=2*|x-1|−4 and sketch its derivative graph. Choose a numeric value a=-7, mark the point (a, f(a)) on the function, and compute the derivative value f'(a) to link the slope meaning to this location. Then define a piecewise linear expression that uses f(a)+f'(a)*(x−a) only for x within the interval [a−1, a+1], and display that corresponding line segment as a local approximation. Also include the key reference points (1,-2) and (1,2) to highlight the vertical symmetry at x=1, and show the derivative curve clearly alongside the local segment.
The prompt above was compiled from the original drawing commands and is for reference only.