Let f : [1, ∞) → be a differentiable function such that and 3 _ 1 ^ x f(t) d t=x f(x)- x^…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f : [1, ∞) → 
be a differentiable function such that 
and \(3 \int_{1}^{x} f(t) d t=x f(x)-\frac{x^{3}}{3} x \in[1, \infty) .\)
Let e denote the base of the natural logarithm. Then the value of f (e) is
be a differentiable function such that and \(3 \int_{1}^{x} f(t) d t=x f(x)-\frac{x^{3}}{3} x \in[1, \infty) .\) Let e denote the base of the natural logarithm. Then the value of f (e) is
Answer
(C)
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