(2)
令f(x)=4 當x=1
f(x)=10 當x=3
f(x)=-x 當x不等於1和3的實數
則 f has at least one minimum for some x in the interval (1,3).好像不成立
(4)
這題既然問是否 continuous on the all real line 就要定義f(1)的值吧
f(x)=|x-1| / (x-1)
則
limx趨近1正f(x)= x-1 / (x-1)=1
limx趨近1負f(x)= 1-x / (x-1)=-1
limx趨近1正f(x)不等於limx趨近1負f(x)
若給f(1)有定義則 f(x)在x=1不連續