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JEE Main202125 Jul 2021Evening ShiftMathematicsApplication of DerivativesActual

Let a curve y = f x pass through the point 2 , log e 2 2 and have slope 2 y x log e x for all positive real values of x . Then the value of f e is equal to _____.

Correct answer

0

Step-by-step solution

Let a curve y = f x pass through the point 2 , log e 2 2 and have slope 2 y x log e x for all positive real values of x . Therefore, y ' = 2 y x ln x ⇒ d y y = 2 d x x ℓ n x ⇒ ℓ n y = 2 ℓ n ℓ n x + C Put x =2 , y = ℓ n 2 2 ⇒ c = 0 ⇒ y = ℓ n x 2 ⇒ f e = 1 .

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