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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

Options

  1. Aπ
  2. B2 π
  3. C3 π 2
  4. Dπ 2

Correct answer

C. 3 π 2

Step-by-step solution

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

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