Bellwork – Show right and explain one wrong!

1. Bellwork – Show right and explain one wrong!

2. Questions About Functions • There are lots of questions we can ask about functions! Here are three of them: • Where is this function convex or concave? • Where is this function increasing or decreasing? • Where are the maximum and minimum values of this function? • We want to be able to answer these questions for any function.

3. Increasing and Decreasing • ITS All About JOE • We mark and record the interval on the X axis.

4. Convex or Concave • The graph of a concave function looks like a Hill. • The graph of a convex function looks like a Valley.

5. Convex or Concave • It’s also possible for a graph to be neither concave nor convex.

6. You Try! • Is this graph concave, convex, or neither? • On which interval(s) is the graph increasing? • On which interval(s) is the graph decreasing?

7. You Try! • Is this graph concave, convex, or neither? • On which interval(s) is the graph increasing? • On which interval(s) is the graph decreasing?

8. You Try! • Is this graph concave, convex, or neither? • On which interval(s) is the graph increasing? • On which interval(s) is the graph decreasing?

9. Minimum and Maximum • The highest and lowest points on a graph are called the maximum and minimum. • The global maximum and global minimum are the highest and lowest points over the entire domain. • A local maximum and local minimum are the highest and lowest points over a certain interval. • These are displayed as a point

10. Maximum and Minimum • Find all local minimum and maximum values. • Is there a global maximum? • Is there a global minimum?

11. Maximum and Minimum • Find all local minimum and maximum values. • Is there a global maximum? • Is there a global minimum?

12. Lets Make a big table !!!

13. Homework