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Math Help - Curvature Question

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    Curvature Question

    I was asked by my teacher "What is the curvature of a 2-D curve at an inflection point? Why?" Can someone help me with this one? I'm absolutely at a loss as how to proceed with this. Thanks.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    I was asked by my teacher "What is the curvature of a 2-D curve at an inflection point? Why?" Can someone help me with this one? I'm absolutely at a loss as how to proceed with this. Thanks.
    isn't curvature defined in terms of the second derivative? what is the value of the second derivative at an inflection point? what does this say about its curvature?
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    Quote Originally Posted by Jhevon View Post
    isn't curvature defined in terms of the second derivative? what is the value of the second derivative at an inflection point? what does this say about its curvature?

    Hmmmm... at an inflection point is when the signs change from negative to positive so that means 0 slope which means no curvature. Did I at least close?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    Hmmmm... at an inflection point is when the signs change from negative to positive so that means 0 slope which means no curvature. Did I at least close?
    what changes from negative to positive? and it is the first derivative that deals with slope, not the second, so no
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    Quote Originally Posted by Jhevon View Post
    what changes from negative to positive? and it is the first derivative that deals with slope, not the second, so no

    Ok let me try again. At an inflection point is where concavity changes...... soo.... uhhmm may I have another hint?


    Edit : Just thought of this but since inflection points are where the concavity changes, wouldn't it be a straight line at that inflection point so that'll mean no curvature at all?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    Ok let me try again. At an inflection point is where concavity changes...... soo.... uhhmm may I have another hint?


    Edit : Just thought of this but since inflection points are where the concavity changes, wouldn't it be a straight line at that inflection point so that'll mean no curvature at all?
    yes, the second derivative is zero at points of inflection, thus we have zero curvature. that's pretty much it
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    Thanks!!!!
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