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The smallest positive integral value of a , such that the function f x = x 4 - 4 a x 2 + 10 has more than two local extrema, is

Options

  1. A1
  2. B2
  3. C4
  4. D16

Correct answer

A. 1

Step-by-step solution

f ′ x = 4 x 3 − 8 a x = 4 x x 2 - 2 a = 4 x x - 2 a x + 2 a Hence, f x has 3 local extrema if 2 a is real i.e., 2 a > 0 ⇒ a > 0 ∴ Value of minimum a = 1

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