Chapter 7, Problem 1CCE

Give an example of a level curve of a function of two variables.

To determine

An example of a level curve of a function of two variables.

Answer to Problem 1CCE

Solution:

$y=3+\frac{x^2}{2}$ is an example of a level curve of a function of two variables.

Explanation of Solution

Given information:

Instruction to state an example of a level curve of a function of two variables

Explanation:

Let $f(x,y)=-x^2+2y$

The level curve at height $6$ for the function $f(x,y)$ is the graph of $f(x,y)=6$ or $-x^2+2y=6$

Solve for $y$.

$\Rightarrow 2y=6+x^2$

$\Rightarrow y=3+\frac{x^2}{2}$

Thus, $y=3+\frac{x^2}{2}$ is an example of a level curve of a function of two variables