My Math Forum Which of the following statements is correct ?

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July 17th, 2019, 05:19 AM   #1
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Which of the following statements is correct ?

This is a question from a college admission exam.
There is a mistake in the attachment. f is derivative not differentiable.
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Last edited by skipjack; July 17th, 2019 at 11:33 AM.

 July 17th, 2019, 02:00 PM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics The inequality says that $f$ can't decrease faster than $f^2 + 1$. So $f$ can't blow up faster than the solution to the differential equation $\dot u = u^2 + 1$ which blows up in finite time. Compute the blow up time and this must be a bound for the blow up "time" for $f$ which is of course $b-a$.

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