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Let f(x) be positive, continuous, and di...

Let `f(x)` be positive, continuous, and differentiable on the interval `(a , b)` and `(lim)_(x to a^+)f(x)=1`,`(lim)_(x tob^-)f(x)=3^(1/4)`. If `f^(prime)(x)geqf^3(x)+1/(f(x))`, then the greatest value of `(b-a)` is

A

A) `b-agepi//4`

B

B) `b-alepi//4`

C

C) `b-alepi//24`

D

D) None of these

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