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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) = cases 3x-x^2 2 & ; x < 2 [x-1] & ; 2 x < 3 x^2-8x+17 & ; x 3 cases ; then which of the following hold(s) good ? ( [ ] denotes greatest integer function)

Options

  1. A_ x 2 f(x) = 1
  2. Bf(x) is differentiable at x = 2
  3. Cf(x) is continuous at x = 2
  4. Df(x) is discontinuus at x = 3

Correct answer

A. _ x 2 f(x) = 1

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