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Math Help - Concavities

  1. #1
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    Concavities

    When concavities are equal to a number or a constant, what does it mean?

    For example, f''(x) = 3, and f''(x) = 0 when x = 2. What does 2 = 3 mean? And when it is f''(2) = 0 it is a point of inflection correct?
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  2. #2
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    Quote Originally Posted by Barthayn View Post
    When concavities are equal to a number or a constant, what does it mean?

    For example, f''(x) = 3, and f''(x) = 0 when x = 2. What does 2 = 3 mean? And when it is f''(2) = 0 it is a point of inflection correct?
    f''(2) cannot equal 3 and 0 for the same value of x. That's a contradiction. As a result, both of your sentences "For example, f''(x) = 3, and f''(x) = 0 when x = 2." and "What does 2 = 3 mean?" are meaningless.

    The second derivative being zero does not imply that there is a point of inflection. If you know you have a point of inflection, then the second derivative is zero. So the implication only works one way. My favorite mnemonic device for remembering the second derivative test is the following:

    Concavities-second-derivative-test-mnemonic.jpg

    I can answer you better if you refine your questions.
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    f''(2) cannot equal 3 and 0 for the same value of x. That's a contradiction. As a result, both of your sentences "For example, f''(x) = 3, and f''(x) = 0 when x = 2." and "What does 2 = 3 mean?" are meaningless.

    The second derivative being zero does not imply that there is a point of inflection. If you know you have a point of inflection, then the second derivative is zero. So the implication only works one way. My favorite mnemonic device for remembering the second derivative test is the following:

    Click image for larger version. 

Name:	Second Derivative Test Mnemonic.JPG 
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ID:	21577

    I can answer you better if you refine your questions.
    Sorry, when I stated the two examples of f''(x) being equal to something, I meant two different f''(x)'s, not both the same. So If it does not have an x-value, what does it mean?
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