Question

The function f(x) = sin⁴ x + cos ⁴ x increasing if –

• A. 0 < x <π/8
• B. π/4 < x < 3π/8
• C. 3π/8 < x < 5π/8
• D. 5π/8 < x < 3π/4

Answer 1

Answer: (B)

π/4 < x < 3π/8

Answer 2

Here, ƒ(x) = sin⁴ x + cos⁴ x

ƒ′(x) = 4 sin³ x . cos x + 4 cos³ x (– sin x)

ƒ′(x) = 4 sin x cos x (sin² x – cos² x)

ƒ′(x) = 2 (sin 2x) (– cos 2x)

ƒ′(x) = – sin 4x

Now, ƒ′(x) ≥ 0 if sin 4x ≤ 0

⇒ π ≤ 4x ≤ 2π 

⇒ π/4 ≤ x ≤ π/2

Here (2) is only subset of $\left\lbrack \frac{\pi}{4},\frac{\pi}{2} \right\rbrack$

Therefore, (2) is the solution.