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MHT CET2016MathematicsApplication of Derivatives

If Rolle's theorem for a function f x = e x sin ⁡ x - cos ⁡ x is verified on π 4 , 5 π 4 then the value of c is

Options

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

Correct answer

D. π

Step-by-step solution

Given, f x = e x ( sin ⁡ x - cos ⁡ x ) ∴ f ′ x = e x cos ⁡ x + sin ⁡ x + sin ⁡ x - cos ⁡ x e x ∴ f ′ x = 2 e x sin ⁡ x To verify Rolle's Theorem. f ′ c = 0 2 e c sin ⁡ c = 0 ⇒ sin ⁡ c = 0 ∴ c = π

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