
Concavity and Points of Inflection
Presentation
•
Mathematics
•
12th Grade
•
Hard
Joseph Anderson
FREE Resource
3 Slides • 5 Questions
1
Concavity
'The curvature of a graph'
2
Concave Up
f looks 'U' shaped
f ' is increasing
f " > 0
3
Multiple Choice
Over what intervals will the second derivative of f(x) be positive?
(−∞,1) and (1,∞)
(1,∞)
(−1,∞)
(−1,∞)
4
Concave Down
f looks 'n' shaped
f ' is decreasing
f " < 0
5
Multiple Choice
Over what intervals will the second derivative of f(x) be negative?
(−∞,−1)
(−∞,1)
(1,∞)
(−1,1)
6
Poll
Where the graph changes concavity is called the...
Point of Interest
Point of Inflection
Point of Concavity
7
Multiple Choice
All 'pretty polynomial' graphs have a point of inflection.
True
False
8
Poll
Check the statements that make the most sense to you...
The graph is always increasing
The graph has no relative extrema
The graph has one point of inflection
The graph has two vertical asymptotes
The graph has one horizontal asymptote
Concavity
'The curvature of a graph'
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