Nice Problem

Sunday 16 May 2004 at 7:28 pm | In Articles | Post Comment

There’s a very nice problem on The University of Warwick Mathematical Society’s site.
I won’t say exactly where because it has the solution there as well 😕

  1. If f is continuously differentiable on the open interval (a,b)
  2. \lim_{x \to a^{+}}f(x)=\infty

  3. \lim_{x \to b^{-}}f(x)=-\infty

  4. f^{\prime}(x)+f(x)^2 \geq 1

then prove that b-a \geq \pi

Stuck!. Then click on read more for a hint

Define g(x)=\tan^{-1}f(x)+x for x \in (a,b)
Look at [Unparseable or potentially dangerous latex formula. Error 4 ]

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