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?• 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?

Lets Make a big table !!!What are we looking for ? How do you do it?

Function?Domain?Range?Symmetry?Increase/ Decreasing?Concave/ Convex?Mins / Maxs

Homework