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JEE Main2012MathematicsApplication of DerivativesActual

Let a, b R be such that the function f given by f(x)= |x|+b x^2+a x, x 0 has extreme values at x=-1 and x=2 . Statement 1: f has local maximum at x=-1 and at x=2 . Statement 2: a = 1 2 and b = -1 4

Options

  1. AStatement 1 is false, statement 2 is true
  2. BStatement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
  3. CStatement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
  4. DStatement 1 is true, statement 2 is false

Correct answer

B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

Step-by-step solution

f^ (x)= 1 x +2 b x+af has extremevalues and differentiable f^ (-1)=0 a-2 b=1f^ (2)=0 a+4 b=- 1 2 a= 1 2 , b=- 1 4 f^ (-1), f^ (2) are negative. f has local maxima at -1,2

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