Question

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

(a) 0 < x < π/8

(b) π/4 < x < 3π/8

(c) 3π/8 < x < 5π/8

(d) 5π/8 < x < 3π/5

Answer 1

Correct option (b) π/4 < x < 3π/8

Explanation:

Given f(x) = sin⁴x + cos⁴x

f'(x) = 4sin³x cosx – 4cos³x sinx

= – 4sinxcosx(cos²x – sin²x)

= – 2(2sinxcosx)(cos²x – sin²x)

= – 2sin2xcosx2x

= – sin4x

f increases when f'(x) > 0