Question $5$:

$(4$ Marks$)$

A$)$ Let $k$ be any real number. Find the value of $k$ such that the function

$f(x)=\{[k{x}^2+2,,x1],[3kx-1,,x<1]\}$

is continuous at $x=1.$

B$)$ Determine whether the mean value theorm can be applied to $f(x)=3+\sqrt[\phantom{2}]{x}$ on $[0,4]$ or not