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Estimating the Derivative of CCD.DE at 0 with h>0

Estimating the Derivative of CCD.DE at 0 with h>0
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2018-01-28 03:17
FunctionCalculusDerivative
This example demonstrates how to estimate the derivative of the exponential function CCD.DE at 0 using a forward difference method. Key mathematical concepts include derivatives and exponential functions. The construction uses vectors, sequences, and functions in GeoGebra.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Sequence((j, f(j)), j, 0, k) → list1
  3. Sequence(Vector[(0, x(Element[list1, j])), (2, y(Element[list1, j]))], j, 1, k) → list2
  4. Vector(C, Y1) → v
  5. Vector(D, Y2) → w
  6. Segment(Y1, Y2) → Δy
  7. Segment(C, D) → Δx

AI Drawing Prompt Reference

Draw a coordinate plane with an exponential function curve near the origin. Place two points on the positive x-axis and draw a vector from the first to the second. Generate a sequence of points at integer x-values starting from 0, compute their function values, and for each point draw a horizontal vector pointing right to the corresponding y-value. Also draw two vectors from near the origin to two points on the curve, then connect those two points with a vertical segment and connect their x-axis projections with a horizontal segment to illustrate the change in y over the change in x.
The prompt above was compiled from the original drawing commands and is for reference only.