If f(x) is a differentiable function in ...

If f(x) is a differentiable function in the interval `(0, oo)` such that `f(1)=1` and `underset(t to x)lim(t^(2)f(x)-x^(2)f(t))/(t-x)=1`, for each `x gt 0` then `f((3)/(2))` is equal to

A

`(13)/(6)`

B

`(23)/(18)`

C

`(25)/(9)`

D

`(31)/(18)`

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