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Let `f(x)` be positive, continuous, and differentiable on the interval `(a , b)a n d lim_(x->a^+)f(x)=1,lim_(x->b^-)f(x)=3^(1/4)dot` If `f^(prime)(x)geqf^3(x)+1/(f(x)),` then the greatest value of `b-a` is (a)`pi/(48)` (b) `pi/(36)` (c)`pi/(24)` (d) `pi/(12)`

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