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Concavity of Functions

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Presentation on theme: "Concavity of Functions"— Presentation transcript:

1 Concavity of Functions

2 Yes And therefore, over this interval, is decreasing What does this say about over this interval?

3 Yes And therefore, over this interval, is increasing What does this say about over this interval?

4 How could we describe the shape of the graph over intervals where
is decreasing? How about “Concave Down”?

5 How could we describe the shape of the graph over intervals where
is increasing? How about “Concave Up”?

6 About where on this graph do the slopes seem to transition from decreasing to increasing?
x = –1 This is called a point of inflection.

7 Point of Inflection The point at which the graph of f changes concavity . At this point or is undefined.

8 Find the intervals over
which f is increasing/decreasing. Find the intervals over which f is concave up/concave down.

9 So let’s test the intervals:
+ + min max

10 So let’s test the intervals:
+

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