Unit 4: Derivatives and Graphs
A visual person should find this unit extremely helpful in understanding the concepts of calculus, as a major emphasis in this unit is to display those concepts graphically. That allows us to see what, so far, we could only imagine. Graphs help us to visualize ideas that are hard enough to conceptualize - like limits going to infinity but still having a finite meaning, or asymptotes - lines that approach each other but never quite get there.
Graphs can also be used in a kind of reverse by displaying something for which we should take another mathematical look. It is hard enough to imagine a limit going to infinity, and therefore never quite getting there, but the graph can tell us that it has a finite value, when it finally does get there, so we had better take a serious look at it mathematically.
Completing this unit should take you approximately 29 hours.
4.1: Finding Maximums and Minimums
4.1.1: Practice Problems
4.2: The Mean Value Theorem and Its Consequences
4.2.1: Practice Problems
4.3: The First Derivative and the Shape of a Function f(x)
4.3.1: Practice Problems
4.4: The Second Derivative and the Shape of a Function f(x)
4.4.1: Practice Problems
Problem Set 6
4.5: Applied Maximum and Minimum Problems
4.6: Infinite Limits and Asymptotes
4.6.1: Practice Problems
4.7: L'Hopital's Rule
4.7.1: Practice Problems
Problem Set 7