lean_workbook_plus_13705

Basic method (there surely exists something smarter) : $y=\frac{2x}{2x-1}$ with $x\in[1,\frac 32]$ \nAnd so we are looking at $\max_{x\in[1,\frac 32]}f(x)$ with $f(x)=x^3+\frac{8x^3}{(2x-1)^3}$ \nAnd it is easy to see that $f(x)$ is continuous convex over the given interval and so result is \n $\max(f(1),f(\frac 32))=9$ \nQ.E.D.