Question

Show that the sum of the x-,y-&z- intercepts of any tangent plane to the surface √x+ √(y )+ √z= √c is a constant.

Answer 1

tangent plane equation:
\[\frac{\partial f}{\partial x}x+\frac{\partial f}{\partial y}y+\frac{\partial f}{\partial z}z=0\]
where f(x,y,z) is surface equation
Later find it's intercepts by setting x=0,y=0 for z-inrcp. And similar for the rest

Answer 2

is z intercept is 0.5?

Answer 3

dind't calculate it.

Answer 4

am i right?