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# Bellwork – Show right and explain one wrong! PowerPoint PPT Presentation

Bellwork – Show right and explain one wrong!. 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?

Bellwork – Show right and explain one wrong!

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### 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.

### Increasing and Decreasing

• ITS All About JOE

• We mark and record the interval on the X axis.

### Convex or Concave

• The graph of a concave function looks like a Hill.

• The graph of a convex function looks like a Valley.

### Convex or Concave

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

### 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?

### 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?

### 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?

### 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

### Maximum and Minimum

• Find all local minimum and maximum values.

• Is there a global maximum?

• Is there a global minimum?

### Maximum and Minimum

• Find all local minimum and maximum values.

• Is there a global maximum?

• Is there a global minimum?