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July 17th, 2019, 05:19 AM  #1 
Newbie Joined: Jul 2019 From: Romania Posts: 1 Thanks: 0  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. 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: 669 Thanks: 440 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 $ba$. 

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