Question

Describe the level surface of the function.

\(f\left( {x,y,z} \right) = x + 3y + 5z\).

Short answer

Answer is not given in the drive

Step-by-step solution

The level curves of the function are of the form:

\(x + 3y + 5z = k\) (\(k \to \)constant)

Step 2: \(k = 0,1,2\)

\(\begin{aligned}{l}x + 3y + 5z &= 0\\x + 3y + 5z &= 1\\x + 3y + 5z &= 2\end{aligned}\)

These represent family of planes. This level curve forms a family of parallel planes because they all passes the same normal vector.

The level curves of the function is shown below: