The function f x = e sin ⁡ x + cos ⁡ x ∀ x ∈ 0 , 2 π attains local extrema at x = α and x = β , then α + β is equal to

Question

The function f x = e sin ⁡ x + cos ⁡ x ∀ x ∈ 0 , 2 π attains local extrema at x = α and x = β , then α + β is equal to, π, 2 π, 3 π 2, π 2

MARKS App · Accepted Answer

f ′ x = e sin x + cos x ⋅ cos x − sin x ∴ f x attains local extrema at x = π 4 , 5 π 4 i.e. α + β = 6 π 4 = 3 π 2