Question

函数Y=ax3的曲率最大点是哪一点

Answer 1

楼上不懂,照他这么说y=x²的曲率处处相等,

曲率

k = y'' / (1 + (y')²)^(3/2)

y = ax³

k = 6ax / (1 + 9·a^2·x^4)^(3/2)

k'(x) = 0解得

x = ±3^(-1/2)·5^(-1/4)·a^(1/2) = ±1/√((√5)·3·a)