Let f x = tan 3 ⁡ x - 3 tan 2 ⁡ x + 1 ,   ∀ x ∈ - π 4 , π 4 . Then, the positive difference between the least value and the local maximum of the function is

Step-by-step solution

Let, tan ⁡ x = t ⇒ t ∈ - 1 , 1   ∵ x ∈ - π 4 , π 4 ∴ f t = t 3 - 3 t 2 + 1 ⇒ f ′ t = 3 t 2 − 6 t = 3 t t − 2 ∴ f - 1 = - 1 - 3 + 1 = - 3 f 1 = 1 - 3 + 1 = - 1 f 0 = 1 ∴ Least value = - 3 Local maximum value = 1 ∴ The positive difference = 4