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!?

Samuel CoskeyNice post! A slope isn’t just a change in distance, but a change in distance relative to a change in time. Velocity has the form $m/s$, meters divided by seconds.

Marc GarlandPost authorYou are certainly correct! I should have been more clear. This has been edited! Thank you for your contributions! I like your post too!

samanthabartlettMarc! Calculus is the bomb! And so is Idaho! Great place to live. Did you know that 63% of Idaho’s land is public?! At least that’s what “Fun Facts about Idaho” says!

Anyway I find this very useful when I’m in Physics. We work mostly with velocity and acceleration so using derivatives come in handy. And I do like that you pointed out that it is a change in distance relating to change in time, just like the slope of a line!