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 Nov3 awarded Tumbleweed Oct27 awarded Teacher Oct27 answered Find the closed form of $\tan\frac{\pi }{64}$ by using the number $2$ only? Oct11 revised Local maxima when multiplying two functions added 39 characters in body Oct11 comment Local maxima when multiplying two functions I see, yes that makes sense. So that question is, when do we find a "bump" in the product? Oct11 awarded Commentator Oct11 comment Local maxima when multiplying two functions sorry what do you mean by f|g? Oct11 revised Local maxima when multiplying two functions restated the question more explicitly Oct11 comment Local maxima when multiplying two functions sure, I'll try, let me know if I can clarify further - I'm still trying to formalise it properly in my head! Oct11 comment Local maxima when multiplying two functions ok so this is definitely one right answer, but I don't think it covers all the possibilities. If for example $g(x)$ is a monotonically increasing/decreasing function in the neighbourhood of 0, then $f(0)g(0)$ should still give a local maximum, right? Oct11 asked Local maxima when multiplying two functions Sep27 awarded Curious Sep26 accepted Proving maximum of dot product using derivatives Sep26 comment Proving maximum of dot product using derivatives This is a really cool argument, thank you very much. In the same way I guess one could prove that for $a \cdot b$ to have a minimum, then $a′$ and $b$ must be parallel. It is a bit cyclical maybe since you need the notion that $a′ \cdot b$=0 for perpendicular vectors here, and $a′ \cdot b$=1 in the parallel case, but I really like the reasoning. One question though, why did you say in the beginning that the dot product is non-zero for non-zero b? Wouldn't it be zero for perpendicular vectors? Sep26 awarded Informed Sep26 comment Proving maximum of dot product using derivatives Sorry my mistake I am going to edit it now Sep26 asked Proving maximum of dot product using derivatives Aug27 accepted Number of sequences in a graph Aug27 revised Number of sequences in a graph edited body Aug27 asked Number of sequences in a graph