Suppose I have two analytic periodic nonconstant function $f(x)$ and $g(x)$ with the same period, such that $0 Is it possible to have $g''f - f''g = 0$ also at that same value of $x$? I'm thinking of "simple" functions like $f(x) = 5 + \sin x$ and $g(x) = 2 - \cos x$. Thanks!
If $g$ and $f$ are periodic nonzero functions, and $g'f - f'g = 0$ at some point $x$, is it possible to have $g''f - f''g = 0$ at that point?
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calculus
real-analysis
analysis
periodic-functions
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0Consider $c + (\sin x)^k$. – 2017-01-19
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0you mean take $f(x) = c_{1} + \sin x$, then $g(x) = c_{2} + (\sin x)^{2}$ for example? But then $f$ and $g$ do not have the same period. I specifically require the periods to be the same for $f$ and $g$. @DanielFischer – 2017-01-19
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0Take $c_1 + (\sin x)^3$ and $c_2 + (\sin x)^5$ for example. – 2017-01-19