$\text{ If }f\left(x\right)=\frac{x^2+1}{\left[x\right]},\left(\right[\text{. }]\text{ denotes the greatest integer function), }1\le x<4\text{, then }$

$\text{ range of }\left.f\text{ is [}2,\frac{17}{3}\right)$

$\text{ the maximum value of }f\left(x\right)\text{ is }\frac{17}{3}$

$\text{ the maximum value of }f\left(x\right)\text{ is }\frac{17}{4}$

$f\text{ is monotonically increasing in }[1,4]$