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Math Help - Finding inflection points

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    Finding inflection points

    Well, I am currently employing myself in finding the inflection points to the function y = 4x^2/(4-x^2). Through the process, the obtain the second derivative
    y" = 32(4+3x^2)/(4-x^2)^3. I know from the definition of inflection points that x = -2 and x = 2 do not fit the criterion of being inflection points, and there are no real zeros; yet clearly, from the graph, I can see that there are changes in concavity. So are the two value, x = 2 and x = -2, pseudo points of inflection?
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    Re: Finding inflection points

    Point of inflection will occur when roots are repeated three times.

    I.e. y = x^3 has a point of inflection at x=0

    y = (x-a)^3 has a point of inflection at x=a

    y = x(x-a)(x-b)^3 has a point of inflection at x=b

    and so on...
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    Re: Finding inflection points

    Quote Originally Posted by Bashyboy View Post
    Well, I am currently employing myself in finding the inflection points to the function y = 4x^2/(4-x^2). Through the process, the obtain the second derivative
    y" = 32(4+3x^2)/(4-x^2)^3. I know from the definition of inflection points that x = -2 and x = 2 do not fit the criterion of being inflection points, and there are no real zeros; yet clearly, from the graph, I can see that there are changes in concavity. So are the two value, x = 2 and x = -2, pseudo points of inflection?
    the curve is concave down on (-\infty,-2) and (2,\infty)

    the curve is concave up on (-2,2)

    note that y is undefined at x = \pm 2 ... a curve cannot have inflection points where it is not defined. Inflection points are points defined on a curve where y'' changes sign.
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