換元.
令√x=t
∵ x∈[1,4]
∴ t∈[1,2]
y=t²-2t=(t-1)²-1
對(duì)稱軸t=1,圖像開口向上,
在(1,+∞）上是增函數(shù)
∴ t=1時(shí),y有最小值-1
t=2時(shí),y有最大值0用導(dǎo)數(shù)這種題用導(dǎo)數(shù)？是啊加一個(gè)導(dǎo)數(shù)y=x-2x^(1/2)y'=1-x^(-1/2)=1-1/√x導(dǎo)數(shù)值恒非負(fù)f(x)是增函數(shù)∴ x=1時(shí)，f(x)有最小值-1，x=4時(shí)，f(x)有最大值0