Graphical Interpretation of Relation between Continuity and Differentiability

Q. If $x=1$ is the point of extrema for $f\left(x\right)=\{\begin{array}{cc}x,& 0<x<1\\ g\left(x\right),& 1\le x<2\end{array},$ then which of the following(s) is(are) correct

1. $g\left(x\right)$ is increasing at $x=1$ and $g\left(1\right)>1$
2. $g\left(x\right)$ is decreasing at $x=1$ and $g\left(1\right)>1$
3. $g\left(x\right)$ is increasing at $x=1$ and $g\left(1\right)<1$
4. $g\left(x\right)$ is decreasing at $x=1$ and $g\left(1\right)<1$

Q. Let $f\left(x\right)=\{\begin{array}{cc}\text{max}\{|x|,x^2\},& |x|\le 2\\ 8-2|x|,& 2<|x|\le 4\end{array}$
Let $S$ be the set of points in the interval $(-4,4)$ at which $f$ is not differentiable. Then $S$ :

1. is an empty set
2. equals $\{-2,-1,1,2\}$
3. equals $\{-2,-1,0,1,2\}$
4. equals $\{-2,2\}$

Q. Let $f\left(x\right)=\{\begin{array}{cc}\text{max}\{|x|,x^2\},& |x|\le 2\\ 8-2|x|,& 2<|x|\le 4\end{array}$
Let $S$ be the set of points in the interval $(-4,4)$ at which $f$ is not differentiable. Then $S$ :

1. is an empty set
2. equals $\{-2,-1,1,2\}$
3. equals $\{-2,-1,0,1,2\}$
4. equals $\{-2,2\}$