Bellwork show right and explain one wrong
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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?

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Bellwork – Show right and explain one wrong!

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Bellwork show right and explain one wrong

Bellwork – Show right and explain one wrong!


Questions about functions

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

Increasing and Decreasing

  • ITS All About JOE

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


Convex or concave

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 concave1

Convex or Concave

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


You try

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 try1

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 try2

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

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

Maximum and Minimum

  • Find all local minimum and maximum values.

  • Is there a global maximum?

  • Is there a global minimum?


Maximum and minimum1

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

Lets Make a big table !!!


Homework

Homework


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