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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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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?
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