By the end of the unit the student will learn that...
First and second derivatives can provide information about the function and its graph including intervals of increase or decrease, local and global extrema, intervals of upward or downward concavity, and points of inflection.
Key features of functions and their derivatives can be identified and related to their graphical, numerical, and analytical representations.
Key features of the graphs of f, f’, and f’’ are related to one another.
The derivative can be used to solve optimization problems, that is, finding a maximum or minimum value of a function over a given interval.
If a function f is continuous over the interval [a, b], and differentiable over the interval (a, b), the Mean Value Theorem guarantees a point within that open interval where the instantaneous rate of change equals the average rate of change over the interval.
Asymptotic and unbounded behavior of functions can be explained and described using limits.