线性方程优化问题示例

GeoGebra 命令及参数

1. LaTeX(steps) → counter
2. LaTeX("\text{Move the slider to solve the problem.}") → text0
3. LaTeX("\text{Use the buttons below to return to the original}\cr\text{problem or randomly generate a similar practice}\cr\text{problem.}") → RandomizationText
4. Corner(2, 3) → topright
5. Corner(2, 1) → bottomleft
6. Sequence(k, k, 2010, 2017, 0.25) → Years
7. LaTeX((((("\text{The graph on the right shows how the value of a stock}\cr\text{has changed over a period of time. What is the}\cr\text{average rate of change from " * startYear) * " to ") * endYear) * "?}")) → Problem
8. LaTeX("\text{Determine the interval to be observed.}") → text1
9. LaTeX((((((((("\text{The interval to be observed is }\textcolor{#000099}{[" * startYear) * ", ") * endYear) * "]}\text{, or}\cr\text{where }\textcolor{#000099}{") * startYear) * " ≤ x ≤ ") * endYear) * "}\text{.}")) → text2
10. LaTeX("\text{Identify the initial point of the interval.}") → text3
11. LaTeX("\text{Identify the endpoint of the interval.}") → text5
12. LaTeX((((((("\text{The }\textcolor{#000099}{x}\text{-value of the initial point is }\textcolor{#000099}{" * startYear) * "}\text{. The}\cr\text{corresponding }\textcolor{#000099}{y}\text{-value is approximately }\textcolor{#000099}{") * y(StartPoint)) * "}\text{.}\cr\text{The coordinates of the initial point of the interval}\cr\text{are about }\textcolor{#000099}{") * StartPoint) * "}\text{.}")) → text4
13. Zip((j, k), j, Years, k, SharePrices) → Data
14. LaTeX((((((("\text{The }\textcolor{#000099}{x}\text{-value of the final point is }\textcolor{#000099}{" * endYear) * "}\text{. The}\cr\text{corresponding }\textcolor{#000099}{y}\text{-value is approximately }\textcolor{#000099}{") * y(EndPoint)) * "}\text{.}\cr\text{The coordinates of the final point of the interval}\cr\text{are about }\textcolor{#000099}{") * EndPoint) * "}\text{.}")) → text6
15. LaTeX("\text{Substitute the coordinates of the two points into the}\cr\text{slope formula to calculate the average rate of change.}") → text7
16. Segment(StartPoint, EndPoint) → f
17. Slope(f) → a
18. If(round(a, 0) ≟ changeRate, LaTeX[(abs(changeRate) * ".00")], LaTeX[(abs(changeRate) * "0")]) → rateText
19. If(a < 0, "-", "") → rateSign
20. TableText({{LaTeX["\textcolor{#000099}{m=\frac{y_2-y_1}{x_2-x_1}}"], LaTeX["\text{Slope formula}"]}}) → text8
21. LaTeX((((((((("\text{The average rate of change for the price of this stock over the interval}\cr\text{[}" * startYear) * ", ") * endYear) * "\text{] is approximately }") * rateSign) * "\$") * rateText) * "\text{ per year.}")) → text12
22. TableText({{LaTeX["\textcolor{#000099}{m=\frac{y_2-y_1}{x_2-x_1}}"], LaTeX["\text{Slope formula}"]}, {LaTeX[(((((((("\textcolor{#000099}{m=\frac{(" * y(EndPoint)) * ")-(") * y(StartPoint)) * ")}{(") * x(EndPoint)) * ")-(") * x(StartPoint)) * ")}}")], LaTeX[(("\text{Substitute }\textcolor{#000099}{" * StartPoint) * "}")]}, {LaTeX["\text{}"], LaTeX["\text{for }\textcolor{#000099}{(x_1,y_1)}"]}, {LaTeX["\text{}"], LaTeX[(("\text{and }\textcolor{#000099}{" * EndPoint) * "}")]}, {LaTeX["\text{}"], LaTeX["\text{for }\textcolor{#000099}{(x_2,y_2)}\text{.}"]}}) → text9
23. TableText({{LaTeX["\textcolor{#000099}{m=\frac{y_2-y_1}{x_2-x_1}}"], LaTeX["\text{Slope formula}"]}, {LaTeX[(((((((("\textcolor{#000099}{m=\frac{(" * y(EndPoint)) * ")-(") * y(StartPoint)) * ")}{(") * x(EndPoint)) * ")-(") * x(StartPoint)) * ")}}")], LaTeX[(("\text{Substitute }\textcolor{#000099}{" * StartPoint) * "}")]}, {LaTeX["\text{}"], LaTeX["\text{for }\textcolor{#000099}{(x_1,y_1)}"]}, {LaTeX["\text{}"], LaTeX[(("\text{and }\textcolor{#000099}{" * EndPoint) * "}")]}, {LaTeX["\text{}"], LaTeX["\text{for }\textcolor{#000099}{(x_2,y_2)}\text{.}"]}, {LaTeX[(((("\textcolor{#000099}{m=\frac{" * rise) * "}{") * run) * "}}")], LaTeX["\text{Subtract.}"]}}) → text10
24. TableText({{LaTeX["\textcolor{#000099}{m=\frac{y_2-y_1}{x_2-x_1}}"], LaTeX["\text{Slope formula}"]}, {LaTeX[(((((((("\textcolor{#000099}{m=\frac{(" * y(EndPoint)) * ")-(") * y(StartPoint)) * ")}{(") * x(EndPoint)) * ")-(") * x(StartPoint)) * ")}}")], LaTeX[(("\text{Substitute }\textcolor{#000099}{" * StartPoint) * "}")]}, {LaTeX["\text{}"], LaTeX["\text{for }\textcolor{#000099}{(x_1,y_1)}"]}, {LaTeX["\text{}"], LaTeX[(("\text{and }\textcolor{#000099}{" * EndPoint) * "}")]}, {LaTeX["\text{}"], LaTeX["\text{for }\textcolor{#000099}{(x_2,y_2)}\text{.}"]}, {LaTeX[(((("\textcolor{#000099}{m=\frac{" * rise) * "}{") * run) * "}}")], LaTeX["\text{Subtract.}"]}, {LaTeX[(("\textcolor{#000099}{m=" * changeRate) * "}")], LaTeX["\text{Divide.}"]}}) → text11