JEE Main 2021 (Online) 26th August Evening ShiftQuestion 1
Let $[t]$ denote the greatest integer less than or equal to $t$. Let $f(x)=x-[x]$, $g(x)=1-x+[x]$, and $h(x)=\min\{f(x),g(x)\}$, $x\in[-2,2]$. Then $h$ is :
Limits & Continuity
Solution
On $[k,k+1)$ with $t=x-k$: $f=t$, $g=1-t$, so $h=\min(t,1-t)$ (a zigzag). At integers $h=0$ and both one-sided limits are $0$, so $h$ is continuous on $[-2,2]$. Corners occur at integers $-1,0,1$ and half-integers $-\tfrac32,-\tfrac12,\tfrac12,\tfrac32$ inside $(-2,2)$: 7 points. So $h$ is continuous but not differentiable at more than four points. Option (C).