**Learning objectives**

- Find maxima and minima of a function using a graph
- Distinguish between local and global extrema
- Use gradient search to find local maxima and minima of a function
- Use the values of first and second derivatives to describe a graph near a critical point
- Use algebra to find a list of critical points where there might be a maximum or minimum value of a function

**Before class**

- Read Hughes-Hallett 4.1, 4.2, 4.3
- Practice problems 4.1: 6, 16, 17, 18, 20, 23; 4.2. 8, 13; 4.3: 2, 17, 19, 40, 47.

**In class**

- Consult main points of the lesson
- Optimize using R
- Practice problems, check by graphing