方向导数与梯度的三维可视化演示
2015-01-07 05:16
本GeoGebra范例演示多元函数f(x,y)的方向导数与梯度概念。通过三维曲面展示某点P处沿方向向量u的方向导数极限定义，涵盖偏导数f_x与f_y的计算、切平面构造及方向曲线的几何意义。用户可借助滑块调整点坐标与方向向量，实时观察切平面、方向导数值及梯度向量的变化，直观理解梯度方向为函数值增长最快方向的核心原理。
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