3-5 Practice: Rate of Change Demo
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Algebra 1|3: Linear Equations
① This example demonstrates a dynamic comparison between the average rate of change and the instantaneous rate of change of a function over an interval. ② Core math concepts include derivatives, limits, function graphs, and rate of change. ③ Construction highlights: Random, Min, Max, and Textfield commands generate random points A1‑A5 and B1‑B5; sliders m, b, a and input boxes InputBox1/2 control line parameters; button1 triggers calculations; list1 and list2 store coordinates; x_min, x_max, y_min, y_max set the view window; pic1 and text1‑3 display the graph and annotations. ④ Suitable for high‑school pre‑calculus or introductory college calculus courses, and for self‑study of rate‑of‑change concepts.
GeoGebra Commands & Parameters
Random(-5, 5) → mRandom(-10, 10) → bMin(list1) → x_{min}Max(list1) → x_{max}Min(list2) → y_{min}Max(list2) → y_{max}Textfield(m_{input}) → InputBox1Textfield(b_{input}) → InputBox2
AI Drawing Prompt Reference
Draw a function curve with five randomly placed point pairs that set the visible x‑ and y‑range; add two adjustable lines — one representing the average rate of change over an interval (secant) and the other the instantaneous rate of change at a point (tangent) — whose slope, intercept, and tangent location can be changed via sliders or input boxes; a button triggers calculation and displays the numeric slopes together with explanatory text annotations, so the whole figure updates dynamically to illustrate the relationship between derivatives and average rates of change.
The prompt above was compiled from the original drawing commands and is for reference only.