Question

Draw a Contour Map of the function showing several level Curves.

\(f\left( {x,y} \right) = \sqrt x + y\)

Short answer

Given:\(f\left( {x,y} \right) = \sqrt x + y\)

To Draw: Draw a Contour Map of the given function showing several level curves.

Step-by-step solution

Assuming A Constant

Given: Considering function of x and y \(f\left( {x,y} \right) = \sqrt x + y\) for level curves.

Solving For Values Of Constant

To Complete the drawing, graph equation with varying values of c as a value of function

\(\sqrt x + y = c\)

To graph this equation, solve for y

\(\sqrt x + y = c\)

\(y = - \sqrt x + c\)

Example: The equation where\(c = 4\) is,

\(y = - \sqrt x + 4\)

Drawing Contour Map

Hence, Contour Map for \(f\left( {x,y} \right) = \s