Question

Find the interval in which function f(x) = sinx+cosx is increasing.

(a) (5π/4, 2π)

(b) [0, π/4) and (5π/4, 2π]

(c) (π/4, -5π/4)

(d) (-π/4, π/4)

The question was posed to me in final exam.

This key question is from Derivatives Application in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (b) [0, π/4) and (5π/4, 2π]

To explain I would say: 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.

The points x = π/4 and x = 5π/4 divide the interval [0, 2π] into three disjoint intervals which are

[0, π/4), (π/4, 5π/4) and (5π/4, 2π].

Therefore on checking the values we get f is increasing in [0, π/4) and (5π/4, 2π].