If f:(0,∞)→R be a continuous and differentiable function, such tha – InterviewSolution

1.	If f:(0,∞)→R be a continuous and differentiable function, such that f3(x)=x∫0t⋅f2(t)dt,f(x)≠0,f(1)=16 for every x>0, then the value of f(6) is
Answer» If $f : (0, \infty) \to R$ be a continuous and differentiable function, such that $f^{3} (x) = x \int 0 t \cdot f^{2} (t) d t, f (x) \neq 0, f (1) = \frac{1}{6}$ for every $x > 0,$ then the value of $f (6)$ is

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