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Black Book Advanced Problems in MathematicsMathematicsApplication of Derivatives

**Paragraph for Question Nos. 12 to 14** The differentiable function y = f(x) has a property that the chord joining any two points A(x₁, f(x₁)) and B(x₂, f(x₂)) always intersects y-axis at (0, 2x₁ x₂) . Given that f(1) = -1 , then : In which of the following intervals, the Rolle's theorem is applicable to the function F(x) = f(x) + x ?

Options

  1. A[-1, 0]
  2. B[0, 1]
  3. C[-1, 1]
  4. D[0, 2]

Correct answer

B. [0, 1]

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