idontknow Dec 2015 975 128 Earth Nov 15, 2019 #1 Find the maximal value of function \(\displaystyle F(x,y,z)=\sin(xy)\cdot \sin(yz)\cdot \sin(xz)\).

D DarnItJimImAnEngineer Jun 2019 493 262 USA Nov 15, 2019 #2 $\displaystyle x=y=z=\sqrt{\frac{\pi}{2}} \rightarrow F=1$ Reactions: skeeter, topsquark and idontknow

skeeter Math Team Jul 2011 3,293 1,778 Texas Jan 23, 2020 #4 idontknow said: What is the method ? Click to expand... observation ... Reactions: idontknow

romsek Math Team Sep 2015 2,891 1,615 USA Jan 23, 2020 #5 We know that each term has a maximum value of 1 so the product has a max value of 1. We just need to demonstrate that the product does in fact reach 1. Thus we need to solve for $x y = x z = y z = \dfrac{\pi}{2}$ certainly a solution is $x = y = z = \sqrt{\dfrac \pi 2}$ and we only need one Reactions: idontknow and topsquark

We know that each term has a maximum value of 1 so the product has a max value of 1. We just need to demonstrate that the product does in fact reach 1. Thus we need to solve for $x y = x z = y z = \dfrac{\pi}{2}$ certainly a solution is $x = y = z = \sqrt{\dfrac \pi 2}$ and we only need one