Find the intervals in which the function f given by

f (x) = sinx + cosx, o≤x≤2pi is strictly increasing or strictly decreasing

Y = sin x + cos x

f' (x) = cos x - sin x

The function is increasing when:

cos x - sin x (is greater than) 0 / : sin x

cot x - 1 (is greater than) 0

cot x (is greater than) 1

Function is strictly increasing for x∈ (0, π/4) ∪ (π, 5π/4)

Function is strictly increasing for x ∈ (π/4, π) ∪ (5π/4, 2π).