 Created By Ms. Kondo

The Ramp Lab in Chapter 2 raised an important question: How can we find a precise rate of change at a given instant (called the instantaneous rate of change)? Studying rates of change also raises some new areas of focus. How is the rate of change changing? Is the rate of change for all functions the same? How can we generalize the rate of change of a function at an instant?
In this chapter, you will:
Find slope functions for most Parent Graphs both graphically and analytically.
Derive and use the formal definition of a derivative as the limit of the slope of a secant line.
Find derivatives of sine, cosine, and formalize the Power Rule.
Discover what 1st and 2nd indicate about a function’s shape, including where it is increasing, decreasing and its concavity.
Sketch f '(x) and f "(x) from f (x) .
Connect derivatives and second derivatives with velocity and acceleration.
Antidifferentiate.
Investigate and categorize functions that are not differentiable everywhere.
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