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

Question

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, π 3, π 2, 3 π 4, π

MARKS App · Accepted Answer

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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