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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) = cases x^2 + a ; & 0 x < 1 -2x + b ; & 1 x 2 cases and g(x) = cases 3x + b ; & 0 x < 1 x^3 ; & 1 x 2 cases If derivative of f(x) w.r.t. g(x) at x = 1 exists and is equal to , then which of the following is/are correct ?

Options

  1. Aa+b = -3
  2. Ba-b = 1
  3. Cab = 3
  4. D-b = 3

Correct answer

A. a+b = -3

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