Concavity of Functions

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Presentation transcript:

Concavity of Functions

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

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

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

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

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

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

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

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

So let’s test the intervals:  +