Study Abstract

After birth, an infant is known to lose weight for a few days before starting to grow. We make use of this information in order to develop a mathematical lesson that illustrates the concept minimum of a function. At the same time, this lesson will allow one to learn the use of calculus in real situations.

When monitoring the health of a newborn baby, it is very important for a medical practitioner to know, roughly, when a baby should stop losing weight. For, if a baby continues to lose weight beyond the day determined by available medical data, that may be worrisome and measures should be taken to ensure the well-being of the baby.

 First, we will suppose that the functional relationship between the weight of a baby and the number of days from birth is known. How does one obtain such a relationship? Then, we will estimate the day on which the weight of the baby will be the lowest (minimum) using a trial and error approach. Will this be a good estimate? We will demonstrate how to employ the idea of "derivative" (What is a derivative of a function?) from calculus to systematically find the day (from birth) on which the minimum weight occurs. Also, we will present deriviative-free and algebraic methods. Then, we will determine that minimum weight. The newborn baby will start to grow beyond the day on which the minimum weight occurs.