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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) = cases (x, x^2) & x 0 (2x, x - 1) & x < 0 cases , then which of the following is not true ?

Options

  1. Af(x) is not differentiable at x = 0
  2. Bf(x) is not differentiable at exactly two points
  3. Cf(x) is continuous everywhere
  4. Df(x) is strictly increasing , x R

Correct answer

B. f(x) is not differentiable at exactly two points

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