Let f x = sin 4 ⁡ x + cos 4 ⁡ x . Then, f is an increasing function in the interval:

Question

Let f x = sin 4 ⁡ x + cos 4 ⁡ x . Then, f is an increasing function in the interval:, ] 5 π 8 , 3 π 4 [, ] π 2 , 5 π 8 [, ] π 4 , π 2 [, ] 0 , π 4 [

MARKS App · Accepted Answer

f x = sin 4 ⁡ x + cos 4 ⁡ x f ′ x = 4 sin 3 ⁡ x cos ⁡ x + 4 cos 3 ⁡ x - sin ⁡ x = 4 sin ⁡ x cos ⁡ x sin 2 ⁡ x - cos 2 ⁡ x = - 2 sin ⁡ 2 x cos ⁡ 2 x = - sin ⁡ 4 x f x , is increasing when f ′ x > 0 ⇒ - sin ⁡ 4 x > 0 ⇒ sin ⁡ 4 x 0 ⇒ π 4 x 2 π ⇒ π 4 x π 2 ⇒ x ∈ π 4 , π 2

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