Let f:R→R and g:R→R be respectively given by f(x)=|x|+1 and g(x)=x²+1. Define h:R→R by h(x)=max{f(x),g(x)} if x≤0 and h(x)=min{f(x),g(x)} if x>0. Then the number of points at which h(x) is not differentiable is

Case 1: When x<0
f(x)=-x+1 and g(x)=x²+1
At the meeting point f(x)=g(x)
x²+1=-x+1
⇒x(x+1)=0
x=0, -1
⇒y=2
g(x) and f(x) meet at point (-1,2)
Similarly in Case 2: when x≥0
f(x)=g(x) ⇒x+1=x²+1
⇒x²-x=0
⇒x=0,1
Meeting points are (0,1) and (1,2)
From the figure
If x<-1 ⇒max{f(x),g(x)}=g(x)
If -1<x<0 ⇒max{f(x),g(x)}=f(x)
If 0<x<1 ⇒min{f(x),g(x)}=g(x)
If x>1 ⇒min{f(x),g(x)}=f(x)
Therefore, Non-differential points are (0,1), (-1,2) and (1,2)
Correct answer is 3