So I used Lagrange multipliers to find the least distance between the point P(3,4,0) and $$z^2=x^2 + y^2 $$
The points with the least distance turn out to be $$(3/2 , 2 , 4/2 )$$
Now I need to graph the level surface of the objective function f(x,y,z) = minimum value and the constraint. The two surfaces should be tangent to each other. So not sure what it means by f(x,y,z). What are the functions to plot?
The function is $$ f(x,y,z) = x^2 + y^2 - z^2 $$
You want to plot the level surface where $f(x,y,z)=0$ (it's a cone)