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Chapter 12: Q 54 (page 917)

In Exercises 53-58, determine the level surfaces role="math" c=-3,-2,-1,0,1,2,3if they exist for the specified function.

role="math" localid="1653228684646" fx,y,z=-2x-y+4z.

Short Answer

Expert verified

The level surfaces are the planes with equations

-2x-y+4z=c;c=-3,-2,-1,0,1,2,3.

Step by step solution

01

Step 1. Given information

We have given the following function :-

fx,y,z=-2x-y+4z.

We have to determine level surfaces c=-3,-2,-1,0,1,2,3for the given function.

02

Step 2. Determine level surfaces 

The given function is :-

fx,y,z=-2x-y+4z.

We know that the level surfaces are determined as :-

fx,y,z=c.

That is we have :-

-2x-y+4z=c.

We know that this is the equation of plane for any value of c.

So that we can conclude that the level surfaces are the planes with equation

-2xy+4z=cforc=-3,-2,-1,0,1,2,3.

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