Our purpose in this blog is to give the opportunity for math lovers (with formal training or with no training) the opportunity to explore fun math problems. We will encourage anyone to post some interesting questions or solutions to some of the posed questions. Even though we dont want to put any restrictions on the type of questions, it will be nice if the questions could be understandable to the untrained and amateur mathematicians.
I propose the first problem: prove that a continuous real-valued function can not have an uncountable number of relative extrema.
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I propose to solve the problem above that, we use a proof by contradiction. So assume that there exits a function that is continuous and has an uncountable number of relative extrema. I suggest we get some contradiction by looking at the derivative of the function.
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