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Bellwork – Show right and explain one wrong!

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- 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.

- ITS All About JOE
- We mark and record the interval on the X axis.

- The graph of a concave function looks like a Hill.
- The graph of a convex function looks like a Valley.

- It’s also possible for a graph to be neither concave nor convex.

- Is this graph concave, convex, or neither?
- On which interval(s) is the graph increasing?
- On which interval(s) is the graph decreasing?

- Is this graph concave, convex, or neither?
- On which interval(s) is the graph increasing?
- On which interval(s) is the graph decreasing?

- Is this graph concave, convex, or neither?
- On which interval(s) is the graph increasing?
- On which interval(s) is the graph decreasing?

- 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

- Find all local minimum and maximum values.
- Is there a global maximum?
- Is there a global minimum?

- Find all local minimum and maximum values.
- Is there a global maximum?
- Is there a global minimum?