# Applications of Derivatives

Last updated 5 years ago

Discipline:
Math
Subject:
Calculus
10,11,12

Applications of Derivatives

Background information/ History of UseDerivatives are a concept that has developed over time, much like phones, vehicles and eating habits. As society changes, our amenities and, yes, our math changes to meet our needs! Mathematicians originally considered the concept of a derivative in an attempt to describe planetary movement and explain the relationship between the location of an object and its velocity. Issac Newton and Gottfried Leibniz are among the earliest mathematicians to delve into the derivative. Even cooler, they did so at the exact same time from two different countries without ever even knowing each other. Click on their faces to the right to learn more about each mathematician!

Modern UsesParticle Motion- Use functions to describe the position, veloicty and acceleration of objects and how these relate to each other. Applications include daily physical movement as well as atomic/planetary movement.Graphs- Use functions to explain the connection between a function and its derivatives. Applications include identifying and classifying extrema, zeros and concavity. Optimization- Use functions to determine the maximum or minimum valued quanitity. Applications include business profit, stock market activity, area/volume, etc. Related Rates- Use functions to describe situtations in which more than one quanitity changes with time. Applications include any situation with multiple variables.

View Some example videos for each application type here.

Particle Motion

Graphs

Optimization

Related Rates