# Describe the level surfaces of the function. f(x,y,z)=x+3y+5z

Describe the level surfaces of the function.
$$\displaystyle{f{{\left({x},{y},{z}\right)}}}={x}+{3}{y}+{5}{z}$$

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mylouscrapza
$$\displaystyle{f{{\left({x},{y},{z}\right)}}}={x}+{3}{y}+{5}{z}$$
So if we have some constant k, then
$$\displaystyle{x}+{3}{y}+{5}{z}={k}$$
Recall that the equation of a plane is $$\displaystyle{a}{x}+{b}{y}+{c}{z}={d}$$, with a surface normal of $$\displaystyle{<}{a},{b},{c}{>}$$. Varying l wi;; result in different parallel planes. So f describes a familly of parallel planes.
Result: family of parallel planes