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JEE Advanced2013MathematicsApplication of DerivativesActual

The number of points in - ∞ , ∞ , for which x 2 - x sin x - cos x = 0 , is:

Options

  1. A6
  2. B4
  3. C2
  4. D0

Correct answer

C. 2

Step-by-step solution

f x = x 2 - x sin x - cos x f ' x = 2 x - x cos x - sin x + sin x = x 2 - cos x We know that, 2 - cos x is positive for all real numbers, now it depends on x . So, f x is increasing if x > 0 f x is decreasing if x 0 f 0 = - 1 f ∞ = ∞ f - ∞ = ∞ So, it is clear that graph cuts the x -axis at two points, so number of solutions are two.

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