[b](a)[/b] Sketch the diagram of the function $f$ if
\[f(x)=4x(1-|x|) , \quad |x| \leq 1.\]

[b](b)[/b] Does there exist derivative of $f$ in the point $x=0 \ ?$

[b](c)[/b] Let $g$ be a function such that
\[g(x)=\left\{\begin{array}{cc}\frac{f(x)}{x} \quad :  x \neq 0\\ \text{ } \\ 4 \ \ \ \ \quad : x=0\end{array}\right.\]
Is the function $g$ continuous in the point $x=0 \ ?$ 

[b](d)[/b] Sketch the diagram of $g.$