"Mathematics is the universal language of the universe and others that are now being discovered" (Edwards 128). Evolutionary discoveries are made on a daily basis because of math. The common operator of the everyday world depends on math. Cars run, buildings stand, and utilities flow, all because of math. The world would seem to serve no purpose as that of a wondering dog without a master. "The laws of the universe are written largely in the language of mathematics" (Hogg 87). Some of the most interesting natural phenomenon involve change and are best described by equations that relate changing quantities.
Simple math (adding, subtracting, multiplying,) constraints the minor nuance of everyday life, however within derivatives a world of change is unveiled. "Because of the derivative dx/dt =f"(t), describes a change involving x, changing with respect to the independent variable t, it is natural that equations involving derivatives have to be used to describe the changing universe" (Bittinger 92). Whether speaking of new discovers in space or those that explore the ocean bottoms, humans have to be prepared to examine all types of new environmental issues in order to take advantage of these results. Derivatives are the tools, which enable this to happen.
In order to explain the concept of a derivative it is important to clarify certain terms that will have to be used frequently throughout the paper. These terms are continuous, function, limit, left-hand approach, right-hand approach, and differentiate. These terms are used in the description and application of derivatives.
In mathematics, the term continuous has much the same use as it does in everyday life. "To say that a function is continuous at a point, x = C, means that there are no interruptions in the graph of f at C" (Larson 143). In layman's terms this means that there are no holes, jumps, gaps, nor any broken points along the graph.
