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JEE Main2007MathematicsContinuity and DifferentiabilityActual

Let f: R R be a function defined by f(x)= Min x+1,|x|+1 . Then which of the following is true?

Options

  1. Af(x) 1 for all x R
  2. Bf(x) is not differentiable at x=1
  3. Cf(x) is differentiable everywhere
  4. Df(x) is not differentiable at x=0

Correct answer

C. f(x) is differentiable everywhere

Step-by-step solution

f(x)= x+1,|x|+1 f(x)=x+1 x R .

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