Question

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

• A. is an empty set
• B. equals {-2, -1, 1, 2}
• C. equals {-2, -1, 0, 1, 2}
• D. equals {-2, 2}

Answer 1

Answer: (C)

$\{\begin{array}{ll}8+2x,& -4\le x<-2\\ x^2,& -2\le x\le -1\\ |x|,& -1<x<1\\ x^2,& 1\le x\le 2\\ 8-2x,& 2<x\le 4\end{array}$
$f(x)$ is not differentiable at $x=\{-2,-1,0,1,2\}$
$\Rightarrow S=\{-2,-1,0,1,2\}$