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MHT CET202314 May 2023Evening ShiftMathematicsApplication of DerivativesActual

Let f (x)=5-|x-2| and g (x)=|x+1|, x R If f (x) attains maximum value at and g (x) attains minimum value at , then _ x - (x-1) (x^2-5 x+6 ) x^2-6 x+8 is equal to

Options

  1. A1 2
  2. B-3 2
  3. C-1 2
  4. D3 2

Correct answer

A. 1 2

Step-by-step solution

aligned & |x-2| 0 & -|x-2| 0 & 5-|x-2| 5 aligned Maximum value of f (x) is 5 . aligned & 5-|x-2|=5 & |x-2|=0 & x=2 & =2 & |x+1| 0 aligned Minimum value of g (x) is 0 . aligned & |x+1|=0 & x=-1 & =-1 aligned aligned & _ x - (x-1) (x^2-5 x+6 ) x^2-6 x+8 = & _ x 2 (x-1)(x-2)(x-3) (x-2)(x-4) = & _ x 2 (x-1)(x-3) x-4 = & (1)(-1) -2 = & 1 2 aligned

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