Let f ( x ) = 5 - | x - 2 | and g x = x + 1 , x   ∈   R . If f ( x ) attains maximum value…

Let f(x)=5-|x-2| and gx=x+1, x ∈ R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then limx→-αβx-1x2-5x+6x2-6x+8 is equal to
  1. 32
  2. 12
  3. -32
  4. -12

Solution

Maxima of fx will occur at x=2 i.e., α=2

Minima of g(x) will occur at x=-1 i.e. β=-1

∴ limx→2(x-1)(x-2)(x-3)(x-2)(x-4)=12.

Asked in: JEE Main 2019 (12 Apr Shift 2)

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