1.
The learner will develop graphing skills by:
- Recognizing and graphing circles from their equations;
- Graphing lines by using their slopes;
- Identifying and defining functions;
- Determining the domain and range of functions;
- Graphing functions;
- Manipulating functions and their graphs;
- Developing linear models of analytic data;
- Recognizing families of functions from both equations and graphs.
2.
The learner will put to use the idea of limits of a function by:
- Explaining what is meant by a limit of a function;
- Finding one and two sided limits of functions at specific points;
- Finding limits of functions at +00, -00
- Understanding the different types of indeterminate forms;
- Applying L'Hospital's Rule to limits involving the various indeterminate forms.
3.
The learner will put to use the idea of continuity of a function by:
- Stating what is meant by "a function is continuous at a point";
- Stating what is meant by "a function is continuous over an interval";
- Determining the continuity of functions.
4.
The learner will demonstrate an understanding of the derivative by:
- Finding the slopes of tangent lines to functions at specific points.
- Defining the derivative;
- Determining the differentiability of functions;
- Using the delta process to find derivatives of polynomial functions;
- Using differentiation rules to find derivatives of polynomial and trigonometric functions;
- Solving problems using implicit differentiation;
- Applying the derivative to related rate problems.
5.
The learner will analyze functions and graphs by:
- Stating where functions are increasing or decreasing;
- Finding inflection points of functions;
- Applying the first and second derivative tests to determine relative extrema of functions;
- Applying the first and second derivative tests to determine absolute extrema of functions.
6.
The learner will use derivatives to solve applied problems from areas of science, engineering, and business by:
- Applying maximum and minimum techniques to problems;
- Determining velocity and acceleration of objects moving along a line;
- Making use of Newton's method of approximating the roots of an equation;
- Making use of the Mean-Value Theorem.
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