Question

The function f(x) = sin⁴x + cos⁴x increases if –

• A. 0 < x <$\frac{\pi}{8}$
• B. $\frac{\pi}{4}$< x <$\frac{3\pi}{8}$
• C. $\frac{3\pi}{8}$< x <$\frac{5\pi}{8}$
• D. $\frac{5\pi}{8}$< x <$\frac{3\pi}{4}$

Answer 1

Answer: (B)

$\frac{\pi}{4}$< x <$\frac{3\pi}{8}$

Answer 2

f '(x) = 4.sin³x.cosx – 4.cos³x. sin x > 0

= 4 . sin x . cos x (sin²x – cos²x) > 0

= – sin 4 x. > 0

= sin 4x < 0

̃ p < 4x < 2p

̃ $\frac{\pi}{4}$ < x < $\frac{\pi}{2}$

(2) is subset of this solution.