求函数y=ax2-2x+1在区间[0,1]上的最小值

2025-04-08 18:46:53
推荐回答(1个)
回答1:

y=ax^2-2x+1
=a(x -1/a)^2 + 1-1/a^2
(1)当a ≤0时,
y=ax2-2x+1在区间[0,1]上的最小值,ymin =y(0) = 1
(2)当0<1/a<1即a>1时,
y=ax^2-2x+1在区间[0,1]上的最小值,ymin =y(1/a)= 1-1/a^2
(3)当1/a≥1,即 0 y=ax^2-2x+1在区间[0,1]上的最小值,ymin =y(1) =a-1