Manipal Entrance Test 2016 Math Paper

h(x)=min(x,x2) ={

x,	x<0
x2,	0≤x<1
x,	x≥1

It is evident from the above graph that the given function is continuous for all x.
since, there are sharp edges at x=0 and x=1, the function is not differentiable at these points.
Also, at x≥1, the function represents a straight line having slope 1, therefore h′(x)=1,∀x≥1