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The smallest natural value of a for which the function f x = 2 x + 1 - a 2 - x + 2 a + 1 ln ⁡ 2 x - 6 is increasing ∀ x ∈ R , is

Correct answer

1

Step-by-step solution

f ′ x = 2 x + 1 + a 2 − x + 2 a + 1 ln 2 = ln ⁡ 2 2 - x 2 x + a 2 x + 1 + 1 Since f x is an increasing function ∀ x ∈ R ⇒ f ' x ≥ 0 ⇒ a > 0 ∴ The smallest natural value of a = 1

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