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

wurmiana6d 2021-11-13 Answered
Describe the level surfaces of the function.
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={x}+{3}{y}+{5}{z}\)

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mylouscrapza
Answered 2021-11-14 Author has 9413 answers
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={x}+{3}{y}+{5}{z}\)
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
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