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最大体积问题

最大体积问题
几何画板及绘图内容加载中，请稍等……
2018-12-20 02:45
测试改名0函数立体几何微积分最值优化
①本范例演示如何通过调整三角形底边长度和高度，在给定周长下最大化三棱柱的体积；②涉及核心数学概念包括体积计算、均值不等式、指数函数、三角形性质、方程求解；③构造过程中运用了 Sequence（序列）、Point（点）、Polygon（多边形）、Rotate（旋转）、Prism（棱柱）、LaTeX（公式显示）、TableText（表格文本）、Vector（向量）等 GeoGebra 命令与对象；④适合高中立体几何与微积分教学，用于理解最值优化问题。

GeoGebra 命令及参数

  1. Sequence((i, 0), i, x(Box1Anchor), x(Box1Anchor) + pLength / 2, 0.1) → xPoints
  2. Point(xPoints) → X
  3. Polygon(Box1Anchor, Box1Anchor + (0, pLength), Box1Anchor + (pWidth, pLength), Box1Anchor + (pWidth, 0)) → paper, f, g, h, i
  4. Polygon(Box1Anchor, Box1Anchor + (boxWidth, 0), 4) → Box1, j, k, l, m, A, B
  5. Polygon(Box2Anchor, B2, 4) → Box2, n, p, q, r, C, D
  6. Polygon(Box3Anchor, Box3Anchor + (boxWidth, 0), 4) → Box3, s, t, a, b, E, F
  7. Polygon(Box4Anchor, Box4Anchor + (boxWidth, 0), 4) → Box4, c, d, e, f_1, G, H
  8. Rotate(T1, 90°, B1, yAxis) → T1'
  9. Polygon(B1, B2, B3, B4) → pBase, b1, b2, b3, b4
  10. Prism(pBase, T1') → o, I, edge2, edge3, edge4, edge5, edge6, edge7, edge8, J, K, face1, face2, face3, face4, face5, edge1
  11. LaTeX("X") → xLbl
  12. LaTeX(prismLength) → B6
  13. LaTeX(prismWidth) → B7
  14. LaTeX(prismHeight) → B8
  15. LaTeX(prismVolume) → B9
  16. LaTeX(x(X)) → B5
  17. TableText({A5:A9, B5:B9}, "hr |_") → results
  18. LaTeX("\cellcolor{#ffcc80}\text{\phantom{abcd}X}") → A5
  19. Vector((0, 0, 0), (14, 0, 0)) → xAxisArrow
  20. Vector((0, 0, 0), (0, 12.5, 0)) → yAxisArrow
  21. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc