Question

Find the interval in which function f(x) = sinx+cosx, 0 ≤ x ≤ 2π is decreasing.

(a) (π/4, 5π/4)

(b) (-π/4, 5π/4)

(c) (π/4, -5π/4)

(d) (-π/4, π/4)

I got this question during an interview.

Question is taken from Derivatives Application in portion Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (a) (π/4, 5π/4)

To explain: f(x) = sinx+cosx.

f’(x) = cosx – sinx. Now f’(x) = 0 gives sinx = cosx which gives that x=π/4, 5π/4 as 0 ≤ x ≤ 2π.

Therefore on checking the values we get f is decreasing in (π/4, 5π/4).