A Quick Word About Derivatives
In this chapter we'll study derivatives which offer us a powerful way to study the rate of change of a function. For instance, think about the model of the height of an incoming missile,
g(x) from earlier in the book. The derivative of this model will give us insight into the rate of change of the missile.
This chapter has four parts.
- In the first part, we start out by seeing how the concept of a limit from the previous chapter can help us calculate the "tangent lines" of a function. This will give us very detailed information about how a function changes.
- Next, we'll spend a bit of time defining exactly what the derivative of a function is. This is the first big conceptual speed bump in calculus. I strongly encourage you to go back and forth between the definition and the first application to help yourself solidify your understanding.
- After learning about the concept, we'll proceed to acquiring some algebraic procedural knowledge, and study some shortcuts for calculating derivatives, called the Monkey Rules. However, because Geogebra already knows all the Monkey Rules, we won't bother spending much time with them. In fact, if you only care about understanding calculus, you can skip the algebraic procedural Monkey Rules.
- Finally, we'll wrap up our study by seeing how to use derivatives to accomplish some important quantitative tasks.