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

Question

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,

MARKS App · Accepted Answer

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

Search any question & find its solution

Looking for more such questions to practice?