Surface
$\sqrt{c}=\sqrt{x}+\sqrt{y}+\sqrt{z}$ , $(c>0)$
I found that at $(x_{0},y_{0},z_{0})$ a tangent plane to the surface is :
$\frac{x-x_{0}}{2\sqrt{x_{0}}}+\frac{y-y_{0}}{2\sqrt{y_{0}}}+\frac{z-z_{0}}{2\sqrt{z_{0}}}=\sqrt{C}$
a tangent plane and 3 coordinate axes boundes a pyramide (volume $V$)
I'm trying to find $(x_{0},y_{0},z_{0})$ on a surface that gives a maximum value of $V$
Any suggestions or derections ?