calc notes lecture 16

# calc notes lecture 16 - Conclusion 2 Example 2 Determine...

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Lecture Section Objectives Assignment 16 3.3 Concavity and The Second-derivative Test 3.3: 1, 7, 9-17 odd, 23-33 odd, 47, 65 Understanding Goals: 1. Understand the definition of concavity and points of inflection. 2. Understand how to determine the intervals on which the graphs of functions are concave upward or downward. 3. Understand how to find the points of inflection of the graphs of the function and how to use the second-derivative test to find the relative extrema of functions. 4. Understand the concept of diminishing returns in economics and know how to find it in an input-output model. 1

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Example 1 : Determine the open intervals on which the graph of 2 1 ( ) 1 f x x = + is concave upward or downward. Interval Test Value Sign of f ''( x

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Unformatted text preview: ) Conclusion 2 Example 2 : Determine the open intervals on which the graph of 2 2 1 ( ) 4 x f x x + =-is concave upward or downward. 3 Example 3 : Determine the points of inflection and discuss the concavity of the graph of 3 ( ) ( 4) f x x x =-. 4 Question : Are all points where the second derivative is zero points of inflection? Example 4 : The graph below represents ( 29 f x . On what intervals is ( 29 ' f x positive? Negative? Are there any points where ( 29 '' f x = ? Example 5 : The graph below represents ( 29 ' f x . On what intervals is ( 29 f x increasing? Decreasing? Concave up? Concave down? 5 Example 6 : Find the relative extrema of 5 3 ( ) 3 5 f x x x = -+ . 6...
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## This note was uploaded on 04/17/2008 for the course MAT 111 taught by Professor Fan during the Spring '08 term at Union.

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calc notes lecture 16 - Conclusion 2 Example 2 Determine...

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