y=f(x)=x^2-2ax+1=(x-a)^2+1-a^2,為開(kāi)口向上的拋物線,對(duì)稱(chēng)軸為x=a
對(duì)于-1≤x≤2的定義域,函數(shù)的最大值與最小值與a的取值有關(guān)
當(dāng)a≤-1時(shí),f(x)在[-1,2]上為單調(diào)遞增函數(shù),
∴最小值為f(-1)=1+2a+1=2+2a,最大值為f(2)=4-4a+1=5=4a
當(dāng)-1≤a≤(-1+2)/2=1/2時(shí),f(x)在[-1,2]上先遞減后遞增,且f(-1)f(2)
∴最小值為頂點(diǎn),即f(a)=1-a^2,最大值為f(-1)=2+2a
當(dāng)a≥2時(shí),f(x)在[-1,2]上為單調(diào)遞減函數(shù),
∴最小值為f(2)=4a,最大值為f(2)=2+2a