Engineering
Mathematics
Important Points on Derivability
Question

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  x0min    {f(x),  g(x)}      if  x>0.

The number of points at which h (x) is not differentiable is

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Solution

Define, h (x) =  {x2+1;   x<1x+1;  1x<0x2+1;   0x1x+1,  x>1

Clearly, h(x) is non-differentiable at 3 points viz.  x = – 1, 0, 1.