MixedHardQuestion 310016
Question
The interval in which f(x) = sin x + cos x is increasing on [0, 2π] is:
- A[0, π/4]Correct
- B[π/4, 5π/4]
- C[0, π/2]
- D[π, 2π]
Correct answer
[0, π/4]
Explanation
f'(x) = cos x − sin x. f'(x) > 0 when cos x > sin x, i.e., tan x < 1, i.e., x ∈ [0, π/4) ∪ (5π/4, 2π]. So on [0,2π], increasing on [0, π/4] (and [5π/4, 2π]).