Question

Let $[t]$ denote the greatest integer less than or equal to $t$. Let $f(x)=x−[x],g(x)=1−x+[x]$, and $h(x)=\min \{f(x),g(x)\},x∈[−2,2].$ Then $h$ is :

• A. continuous in $[−2,2]$ but not differentiable at more than four points in $(−2,2)$
• B. not continuous at exactly three points in $[−2,2]$
• C. continuous in $[−2,2]$ but not differentiable at exactly three points in $(−2,2)$
• D. not continuous at exactly four points in $[−2,2]$

Answer 1

Answer: (A)

$\min \{x−[x],1−x+[x]\}$
$h(x)=\min \{x−[x],1−[x−[x])\}$

$⇒$ always continuous in $[−2,2]$
but non differentiable at $7$ Points