$(15$ points$)$ Consider the function defined by$,$

$f(x)=\{\begin{array}{ccc}3x+\text{a}& \text{w}\text{h}\text{e}\text{n}& x2\\ 2x^2+4bx+2& \text{w}\text{h}\text{e}\text{n}& x>2\end{array}$

$($a$)$ Find the values for the parameters a and binR such that the function is differentiable for any xinR. State clearly the conditions you use. $($do not use derivative rules, just use limits$).$

$($b$)$ With the same values of a and b previously found, show that the function $g(x)=f^{\text{'}}(x)$ is not smooth.