m110_5.3

# m110_5.3 - Acceleration and the Second Derivative The...

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Acceleration and the Second Derivative The acceleration of a moving object is the derivative of its velocity (the second derivative of the position function.) Function notation:

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Second Derivative
Concavity Let f be a differentiable function on ( a , b ). concave upward concave downward 1. f is concave upward on ( a , b ) if is increasing on ( a , b ). That is, for each value of x in ( a , b ). 2. f is concave downward on ( a , b ) if is decreasing on ( a , b ). That is, for each value of x in ( a , b ).

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Inflection Point A point on the graph of f at which concavity changes is called an inflection point . To find inflection points, find any point, c , in the domain where is undefined. changes sign from the left to the right of c, If then ( c,f ( c )) is an inflection point of f .
The Point of Diminishing Returns Let S be a sales function. Where the graph of S is concave up, monthly sales are increasing; more units are being sold each month than the month before. Where the graph of S is concave down, monthly sales are decreasing; fewer units

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## This note was uploaded on 09/09/2011 for the course MATH 110 taught by Professor Staff during the Spring '11 term at S.F. State.

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m110_5.3 - Acceleration and the Second Derivative The...

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