Let f(x) be positive, continuous, and differentiable on the interval ( – InterviewSolution

1.	Let f(x) be positive, continuous, and differentiable on the interval (a,b) and limx→a+f(x)=1,limx→b−f(x)=31/4. If f′(x)≥f3(x)+1f(x), then the greatest value of b−a is
Answer» Let $f (x)$ be positive, continuous, and differentiable on the interval $(a, b)$ and $lim x \to a^{+} f (x) = 1, lim x \to b^{-} f (x) = 3^{1 / 4} .$ If $f^{'} (x) \geq f^{3} (x) + \frac{1}{f (x)}$ , then the greatest value of $b - a$ is

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