A level curve is a curve on a graph that represents all the points where a function of two variables has the same constant value. For example, in a topographic map, level curves indicate areas of equal elevation, helping to visualize the terrain's shape. These curves are useful in various fields, including mathematics, geography, and engineering. In mathematical terms, if you have a function f(x, y), a level curve for a specific value c is defined by the equation f(x, y) = c. By analyzing these curves, one can understand the behavior of the function and identify critical points, such as maxima, minima, or saddle points.