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

Question

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,

MARKS App · Accepted Answer

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

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