little_wu
春芽
共回答了12个问题采纳率:100% 举报
设:经过X小时后,两船的距离为Y:
Y = √【(20X)²+(82-16X)²】
dY/dX = 【400X-16×(82-16X)】/√【(20X)²+(82-16X)²】
令dY/dX = 0,得到:
400X-16×(82-16X) = 0,400X - 1312 + 256X = 0,X = 2 (小时)
d²Y/dX² = 【400+256】/√【(20X)²+(82-16X)²】-【400X-16×(82-16X)】²/√【(20X)²+(82-16X)²】³
当 X = 2 时,
d²Y/dX² = 【400+256】/√【(40)²+(82-32)²】-【800-16×(82-32)】²/√【(40)²+(82-32)²】³ = 10.2440 > 0
Y最小 = √【(20×2)²+(82-16×2)²】= 10√41 = 64.03 (km)
1年前
11