Let f:[1,∞] be a differentiable function such that f(1)=2. If 6∫1xf(t)dt=3xf(x)−x3 for all x≥1, then the value of f(2) is

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Question

Let $f : [1, \infty]$ be a differentiable function such that $f (1) = 2 .$ If $6 \int_{1}^{x} f (t) d t = 3 x f (x) - x^{3}$ for all $x \geq 1,$ then the value of $f (2)$ is

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Evelyn Discussed

Let

f : [1, \infty]

be a differentiable function such that

f (1) = 2 .

6 \int_{1}^{x} f (t) d t = 3 x f (x) - x^{3}

for all

x \geq 1,

then the value of

f (2)

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Question Text

Let

f : [1, \infty]

be a differentiable function such that

f (1) = 2 .

6 \int_{1}^{x} f (t) d t = 3 x f (x) - x^{3}

for all

x \geq 1,

then the value of

f (2)