The minimum value of the function f x = tan ⁡ x 3 + 2 tan ⁡ x , ∀ x ∈ 0 , π 2 is

Question

The minimum value of the function f x = tan ⁡ x 3 + 2 tan ⁡ x , ∀ x ∈ 0 , π 2 is, 0, 1 2, 1 3, 1 6

MARKS App · Accepted Answer

If x ∈ 0 , π 2 , t a n x ∈ 0 , ∞ Let, tan x = t i.e. y = t 3 + 2 t , t ∈ 0 , ∞ ⇒ 3 y + 2 t y = t ⇒ t = 3 y 1 - 2 y ≥ 0 ⇒ y ∈ 0 , 1 2 Hence, the minimum value of the function = 0

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