Section 15.7 Content Videos

15.7.1: Definitions and Locating Critical Points (16:57)

15.7.2: Classifying Critical Points with the Second Derivative Test (11:41)

15.7.3: Second Derivative Test Example 2 (03:58)

15.7.4: Second Derivative Test Example 3 (05:17)

15.7.5: Second Derivative Test Example 4 (06:44)

15.7.6: Absolute Extrema on Closed and Bounded Regions (22:44)

15.7.7: Absolute Extrema on Closed and Bounded Regions Example 2 (24:54)

15.7.8: Absolute Extrema on Open or Unbounded Sets with Example 1 (08:25)

15.7.9: Absolute Extrema on Open or Unbounded Sets Example 2 (20:34)

Section 15.8 Content Videos

Videos 15.8.1 and 15.8.2 are from Khan Academy because the author does such an amazing job introducing Lagrange multipliers.

15.8.1: Constrained Optimization (06:29)

15.8.2: Lagrange Multipliers (08:42)

15.8.3: Constrained Optimization with Lagrange Multipliers with Example 1 (18:00)

15.8.4: Lagrange Multipliers with Functions of 3 Variables (13:39)

15.8.5: Application of Lagrange Multipliers (11:14)

Practice

Use the practice problems at the end Section 15.7 and 15.8 in our text to practice what you've learned this week. The problems generally increase in difficulty in each subsection. The problems towards the end of the section get increasingly more involved, so I recommend working a few problems from each of the earlier subsections, checking your answers against the back of the book, and then venturing as far as you desire.

Review and Reflect

Take a look at the learning objectives for this week (found in the overview above). After completing everything above, assess how well you feel you meet each objective (say, on a scale from 1-5, 1 being the least comfortable and 5 being confident with having met the objective). The idea here is to make a record of how you feel about each objective so that you can easily go back to it before, say, an exam or at the end of the chapter and easily see what topics you should review. It can also be helpful if you are having trouble understanding a concepts later in the course.

Next Week

Previous Week