My name is Marc and I am a math student at Boise State University in Boise, Idaho which is best known for its potatoes as well as recreational opportunities. One area of mathematics that I enjoy learning and studying about is calculus. Calculus is the study of limits, derivatives, and integrals which are useful in studying continuous functions. Limits play a massive role in a variety of fields ranging from economics to engineering, and limits help to define derivatives. Derivatives are functions that describe the slope of a continuous function. The opposite of a derivative, an integral, can be used to find areas under curves in two dimensions as well as volumes in three dimensions. All of these tools can be used for optimization purposes which are significant in practically any field.

For more information about calculus, you can visit the Wikipedia page here.

Because the derivative represents the slope of a function, the derivative of a function is thus calculated with this idea of change in distance in mind. The equation associated with the derivative is:

$m=\lim_{h\to 0 }\frac{f(a+h)-f(a)}{h}$

Notice that this equation represents a change in distance on a graph. Slopes are meant to represent changes of functions and functions represent a variety of trends! For example, the derivative of a position function in physics would produce a velocity graph which represents speed, or how the distance is changing over time. The derivative of a velocity function would give an acceleration function which reveals how the speed is changing over time. Pretty cool, isn’t it!?