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COMEDK202510 May 2025Morning ShiftMathematicsApplication of DerivativesActual

The least value of ' a ' such that the function x^2+a x+1 is increasing on [1,2] is

Options

  1. A1
  2. B4
  3. C-2
  4. D2

Correct answer

C. -2

Step-by-step solution

Let f(x) = x^2 + ax + 1 . The function f(x) is increasing on the interval [1, 2] if its derivative f'(x) 0 for all x [1, 2] . Calculating the derivative, we get f'(x) = 2x + a . For f(x) to be increasing on [1, 2] , we require 2x + a 0 for all x [1, 2] . This inequality must hold for the minimum value of x in the interval [1, 2] , which is x = 1 . Substituting x = 1 into the inequality, we get 2(1) + a 0 , which simplifies to 2 + a 0 . Therefore, a -2 . The least value of a is -2 . Answer: -2

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