After completing this section, students should be able to do the following.
- Determine a function for velocity, given a function for position.
- Determine a function for acceleration, given a function for position.
- Determine a function for acceleration, given a function for velocity.
- Sketch a detailed graph of a function that includes all relevant extrema, domain restrictions, end-term behavior, curvature, and points of inflection.
- Determine how each of our values (e.g., extrema, curvature, points of inflection) are visually represented on a graph.
- Sketch an example of what linear approximation means for a function.
- Explain the relationship between linear approximation and tangent lines.
- Use linear approximation to approximate values of functions.
- Apply linear approximation when needing an approximate value.
- Determine appropriate functions and anchor values to use when linear approximation is needed.
- Model problems that involve interrelated rates of change.
- Solve problems that involve interrelated rates of change for a desired rate of change.
- Determine optimal solutions to models that require optimization.
- Create a mathematical model based on a problem description that can then be optimized.