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JEE Main201912 Apr 2019Evening ShiftMathematicsApplication of DerivativesActual

Let f ( x ) = 5 - | x - 2 | and g x = x + 1 , x ∈ R . If f ( x ) attains maximum value at α and g ( x ) attains minimum value at β , then l i m x → - α β x - 1 x 2 - 5 x + 6 x 2 - 6 x + 8 is equal to

Options

  1. A3 2
  2. B1 2
  3. C- 3 2
  4. D- 1 2

Correct answer

B. 1 2

Step-by-step solution

Maxima of f x will occur at x = 2 i.e., α = 2 Minima of g ( x ) will occur at x = - 1 i.e. β = - 1 ∴   l i m x → 2 ( x - 1 ) ( x - 2 ) ( x - 3 ) ( x - 2 ) ( x - 4 ) = 1 2 .

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