The problem of segmenting an image into a subject and background has many practical applications, particularly in the fields of machine vision and image classification. This talk will present an avenue to image segmentation via variational calculus. It will follow the intuitive development of the derivative of a functional, present some classic examples from variational calculus and conclude with a particular implementation of such a variational approach for the purpose of image segmentation. This talk will be accessible to those with a background in basic calculus and differential equations.