Question $4$

$(i)$ Let $f$:$RRbe$ defined $as$ follows:

$f(x)=\{\begin{array}{cc}x+3,& x2\\ x-3,& x>2\end{array}$

Determine whether $fis$ differentiable $at2.$

$(ii)$ Find the values $of$ a and $b$ such that $f$:$RR$ defined $by$

$f(x)=\{\begin{array}{cc}ax+b,& x<mn>3</mn>\\ 3x^2-2,& x3\end{array}$

$Is$ differentiable $atx=3.$