Unit Description:
In this unit, scholars will be exposed to the idea of second derivatives and the relationships between the first and second derivatives and the original function. They will be exposed to both the graphical relationships, such as slope and concavity, but also to the applications of speed, velocity, and accelerations when given a distance function. By the end of the unit, scholars should be comfortable not only algebraically evaluating first and second derivatives, but also verbally describing the relationship between a function, its first derivative, and second derivative.
Unit Essential Question: "What are the relationships between a function and its derivatives?"
By the end of the unit, you should be comfortable algebraically, numerically, and graphically identifying:
1) Identifying the changes in the derivatives from an original function.
2) A function's derivatives given the original function
3) The original function given the function's derivatives
4) Describe the relationships between a function, first derivatives, and second derivatives and identify the key characteristics of each.