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Black Book Advanced Problems in MathematicsMathematicsApplication of Derivatives

Let F(x) = (f(x))^2 + (f'(x))^2, F(0) = 6 , where f(x) is a thrice differentiable function such that |f(x)| 1 x [-1, 1] , then choose the correct statement(s)

Options

  1. Athere is atleast one point in each of the intervals (-1, 0) and (0, 1) where |f'(x)| 2
  2. Bthere is atleast one point in each of the intervals (-1, 0) and (0, 1) where F(x) 5
  3. Cthere is no point of local maxima of F(x) in (-1, 1)
  4. Dfor some c (-1, 1), F(c) 6, F'(c) = 0 and F''(c) 0

Correct answer

A. there is atleast one point in each of the intervals (-1, 0) and (0, 1) where |f'(x)| 2

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