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JEE Advanced2008MathematicsApplication of DerivativesActual

Paragraph: Consider the function f:(- , ) (- , ) defined by f(x)= x^2-a x+1 x^2+a x+1 ; 0 Question: Which of the following is true?

Options

  1. Af(x) is decreasing on (-1,1) and has a local minimum at x=1
  2. Bf(x) is increasing on (-1,1) and has a local maximum at x=1
  3. Cf(x) is increasing on (-1,1) but has neither a local maximum nor a local minimum at x=1
  4. Df(x) is decreasing on (-1,1) but has neither a local maximum nor a local minimum at x=1

Correct answer

A. f(x) is decreasing on (-1,1) and has a local minimum at x=1

Step-by-step solution

When x (-1,1) x^2 0 [ 0 < a < 2] f(x) has a local minimum at x=1 .

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