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find the maximum $\frac{\frac{x^2_{1}}{x_{2}}+\frac{x^2_{2}}{x_{3}}+\cdots+\frac{x^2_{n-1}}{x_{n}}+\frac{x^2_{n}}{x_{1}}}{x_{1}+x_{2}+\cdots+x_{n}}$
multivariable-calculus
inequality
optimization
convex-optimization
convexity-inequality
strict convexity attains minimum
real-analysis
calculus
derivatives
convexity-inequality
If $0\le a,b,c\le 1$, then $\frac a{1+bc}+\frac b{1+ac}+\frac c{1+ab}\le 2$
inequality
convexity-inequality
Prove or disprove that the function $f(x)=x^{x^{x^{x}}}$ is convex on $(0,1)$
functions
derivatives
power-towers
convexity-inequality
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