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Math Help - Simple Point of Inflection and Critical Point Question

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    Simple Point of Inflection and Critical Point Question

    Hey I was just wondering if your critical point and point of inflection can be the same?

    Or if you work it out and the Point of inflection turns out the same then, the Point of inflection does not exist? or can the co exist at the same spot?
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    y=x^3 at x=0
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lostsheep View Post
    Hey I was just wondering if your critical point and point of inflection can be the same?

    Or if you work it out and the Point of inflection turns out the same then, the Point of inflection does not exist? or can the co exist at the same spot?
    an inflection point is a point where the concavity changes, this does not happen for other extrema (maximums and minimums), so an inflection point cannot coincide with said critical points

    critical points are points where the first derivative is zero, there are cases when an inflection point fulfills this condition (see curvature's example)
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