level curve of function f(x,y,z)=x+y+z..someone please help me!!!

Question

shamil98 · Answer

I think the first step is to identify the surface given by f(x,y,z) ..

flix · Answer

is it plane??

shamil98 · Answer

I'm not quite sure, I just started calculus 3 myself..

shamil98 · Answer

@dan815 ?

dape · Answer

You get the level curves by setting f(x,y,z) equal to different constant values. So take f(x,y,z)=0 for example, then we have
$$x+y+z=0$$
This is as you guessed the equation for a plane going through the origin with normal $\hat{x}+\hat{y}+\hat{z}$. Different constants will only shift this plane upwards or downwards.

dape · Answer

Oh, and since we are in 3 dimensions the level sets are called level surfaces.

dan815 · Answer

planes

dan815 · Answer

ask more questions i miss calc 3

flix · Answer

Find the equation of the tangent plane to the hyperboloid f(x,y,z)=x^2/a^2 +y^2/b^2 -z^2/c^2 =1 
at (x_0,y_0,z_0 )