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The function f(x) = 1 + |sin x| is:

  1. Continuous and differentiable nowhere
  2. continuous and differentiable everywhere
  3. not differentiable at only x = 0
  4. not differentiable at infinite number of points.

Answer (Detailed Solution Below)

Option 4 : not differentiable at infinite number of points.
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Detailed Solution

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Sin x

F1 Shubham 4.2.21 Pallavi D 1

|sinx|

F1 Shubham 4.2.21 Pallavi D 2

The graph of f(x) = 1 + |sin x| is as shown in the figure:

F1 Shubham 4.2.21 Pallavi D 3

From the graph, it is clear that function is continuous everywhere but not differentiable at integral multiplies of π (∴ at these points curve has sharp turnings).

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