The range of a ∈ R for which the function f x = 4 a - 3 x + log e 5 + 2 a - 7 cot x 2 sin 2 x 2 , x ≠ 2 n π , n ∈ N , has critical points, is :

Step-by-step solution

f x = 4 a - 3 x + log e 5 + 2 a - 7 cot x 2 sin 2 x 2 , x ≠ 2 n π , n ∈ N f x = 4 a - 3 x + log e 5 + a - 7 sin x f ' x = 4 a - 3 1 + a - 7 cos x = 0 ⇒ cos x = 3 - 4 a a - 7 - 1 ≤ 3 - 4 a a - 7 ≤ 1 3 - 4 a a - 7 + 1 ≥ 0         3 - 4 a a - 7 ≤ 1 3 - 4 a + a - 7 a - 7 ≥ 0           3 - 4 a a - 7 - 1 ≤ 0 - 3 a - 4 a - 7 ≥ 0        3 - 4 a - a + 7 a - 7 ≤ 0 3 a + 4 a - 7 ≤ 0