# Max value

#### idontknow

Find the maximal value of function $$\displaystyle F(x,y,z)=\sin(xy)\cdot \sin(yz)\cdot \sin(xz)$$.

#### DarnItJimImAnEngineer

$\displaystyle x=y=z=\sqrt{\frac{\pi}{2}} \rightarrow F=1$

#### idontknow

What is the method ?

Math Team
idontknow

#### romsek

Math Team
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