Question

Find the intervals in which the function f given by

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

Answer 1

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 ).