 Created By Ms. Kondo

So far, you have developed many tools to find derivatives. Since Chapter 3, you have found derivatives using the definition of a derivative as a limit and by using the Power Rule. You have found derivatives by drawing tangents at various points along a curve and describing the slopes of these tangents with a “slope function.” Finally, you have used your graphing calculator to graph using a difference quotient and then identified the resulting slope function.
In Chapter 6, we will complete this set of derivative tools so that you may differentiate all parent graphs. This will include a focus on exponential functions, as well as differentiating those relations that are not functions.
In this chapter, you will:
Revisit exponential functions and study their derivatives.
Explore the mathematical constant “e,” which arises naturally in many contexts.
Use implicit differentiation as a tool to differentiate relations that are not solved explicitly for y.
Find the derivatives of all parent graphs and their inverses.
Develop a process to find the mean value of a function, as well as an average rate of change for a function.
Evaluate improper integrals.
This is a playlist intended to support students who are currently taking a Calculus course using the College Preparatory Mathematics (CPM) curriculum. With a license from CPM, students can access the ebook at: http://textbooks.cpm.org. More information on the CPM Educational Program and curriculum can be found at http://www.cpm.org