In human vision the first level of processing is edge detection. Edges are determined by the transitions from dark points to bright points in an image. For this paper, we consider an edge profile model representing a boundary or edge in an image. From this model we can determine the strength of the edge, the width of the edge, and either the transition from dark to bright to dark or the transition from bright to dark to bright. Our first step was to take the given edge profile and determine the type of edge that is represented and the characteristics of the edge, such as that of the varying width of the edge as the variable a is either increased or decreased. In the next step, we calculated the derivate of the edge profile model. The final step involved utilizing the properties of the function defined by the derivative. Finding the second derivate of the edge profile model allowed us to determine the maximum and minimum values of x for the derivative of the edge profile model.