Modelling with twice continuously differentiable functions

Abstract

Many real life situations can be described using twice continuously differentiable functions over convex sets with interior points. Such functions have an interesting separation property: At every interior point of the set they separate particular classes of quadratic convex functions from classes of quadratic concave functions. Using this property we introduce new characterizations of the derivative and its zero points. The results are applied to the study of sensitivity of the Cobb-Douglas production function. They are also used to describe the least squares solutions in linear and nonlinear regression.

Keywords

• twice continuously differentiable function
• zero derivative point
• separation property of functions
• Cobb-Douglas production function
• least squares solution
• Newton’s second law