Final answer:
To draw a contour map of the function f(x, y) = x^3 - 5y, plot several level curves by choosing different values for the function and solving for y. By plotting these level curves, a contour map of the function can be created.
Step-by-step explanation:
To draw a contour map of the function f(x, y) = x^3 - 5y, we need to plot several level curves. Level curves are curves on the graph where the function has a constant value. To do this, we can choose different values for the function and plot the resulting curves.
For example, if we set f(x, y) = 0, we can solve for y to get y = (x^3)/5. This equation represents a level curve where the function is equal to 0. Similarly, we can choose other values for f(x, y) and plot the corresponding level curves.
By plotting several of these level curves, we can create a contour map of the function.