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

Step-by-step solution

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