Question

Draw a Contour Map of the function showing several level Curves

\(f\left( {x,y} \right) = {x^3} - y\)

Short answer

Given: \(f\left( {x,y} \right) = {x^3} - y\)

To Draw: Draw Contour Map of the function and several level Curves.

Level Curves: The Level Curves of a function f of two Variables are the curves with equation; wherek is a constant.

Step-by-step solution

Assuming A Constant

Level Curves: The Level Curves of a function f of two Variables are the curves with equation; wherekis a constant.

So the level Curves of the given function\(\)\(f\left( {x,y} \right) = {x^3} - y\)is,

\({x^3} - y = k\) ; Where k is a constant

Finding Values Of k And Drawing Level Curves

For \(k = - 2\)

\({x^3} - y = - 2\)

For\(k = 0\)

\({x^3} - y = - 0\)

\(k = 2\)

\({x^3} - y = 2\)

For\(k = - 1\)

\({x^3} - y = - 1\)

For\(k = 1\)

\({x^3} - y = 1\)

Now, Sketch the level Curves as shown below: