Bellwork – Show right and explain one wrong!

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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?

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Presentation Transcript
• 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
• 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?