$(7$ pts$)$ The graph of a function $f(x)$ is given below.

i$)f(x)$ is differentiable at $0.$

ii$)\underset{x{2}^{-}}{lim}f(x)=3.$

iii$)f(x)$ is continuous at $3.$

iv$)$ If $f(x)$ is differentiable at $4,$ then $f^{\text{'}}(4)=0.$

v$)$ There is a root of an equation $f(x)=0$ in the interval $(4,5).$

Choose all of the correct statements.