Inflection Points Practice Problems Solutions

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Mathematics

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Apr 3, 2024

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docx

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Inflection Points Practice Problems At which point(s) does the graph to the right have points of inflection? Points A, C, and D Let f ( x ) = x 3 − 6 x 2 + 12 x . Find the intervals where f is concave up and the intervals where f is concave down. f ' ( x ) = 3 x 2 − 12 x + 12 f '' ( x ) = 6 x − 12 f '' ( x ) = 0 6 x − 12 = 0 6 x = 12 x = 2 Constructing a line test: Concave up: ( 2 ,∞ ) Concave down: (− ∞, 2 )
Inflection Points Practice Problems Consider g ( x ) = 2 x 3 − 3 x 2 − 12 x + 5 . Discuss the concavity of the function. g ' ( x ) = 6 x 2 − 6 x − 12 g ' ' ( x ) = 12 x − 6 g ' ' ( x ) = 0 12 x − 6 = 0 12 x = 6 x = 1 2 Constructing a line test: Concave up: ( 1 2 ,∞ ) Concave down: ( − ∞, 1 2 ) g' ' ( x )
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