題組內容

1. A heat-seeking particle is located at the point (-1,2) on a metal plate whose temperature at (x, y) is T(u,u) = 64-2x² y².

(a) (6 分) In what direction from (-1,2) does the temperature increase most rapidly? What is this rate of increase?

詳解 (共 1 筆)

助人為本

詳解 #7416545

2026/06/22

所以解這題看到increase most rapidly要想到梯度(gradient)

梯度就是偏微

然後化成單位方向向量就是除以長度

然後最大增加率的算法就是

把梯度算出來的開絕對值

ㅤㅤ