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Math Help - what is a critical point

  1. #1
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    what is a critical point

    For example on the graph f(x)= x^3, f'(x)= 3x^2. set it to 0 and u get x=0 does that qualify as a critical point since its not a max or a min, though it changes concavity. do inflection points classify as critical points?
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  2. #2
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    Quote Originally Posted by zintore View Post
    For example on the graph f(x)= x^3, f'(x)= 3x^2. set it to 0 and u get x=0 does that qualify as a critical point since its not a max or a min, though it changes concavity. do inflection points classify as critical points?
    A stationary point of inflection is a critical point.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by zintore View Post
    For example on the graph f(x)= x^3, f'(x)= 3x^2. set it to 0 and u get x=0 does that qualify as a critical point since its not a max or a min, though it changes concavity. do inflection points classify as critical points?
    I have always known "critical points" to be points such that the slope was zero at that point. Inflection points would be critical points of the first derivative.
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    I have always known "critical points" to be points such that the slope was zero at that point.
    Yes, critical points are points where the slope is either zero or undefined...but a stationary point is a type of critical point [point where derivative is 0]. So a statitionary point is a critical point, but not all critical points are stationary points...

    Just a thought to throw out there.

    --Chris
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