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Math Help - Finding minima/maxima/point of inflection

  1. #1
    Member princess_anna57's Avatar
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    Finding minima/maxima/point of inflection

    For f(x) = (2x^2)+(8/x^2) when finding where y = 0 in the first derivative function, it doesn't exist?

    The 1st derivative is f'(x) = 4x - 16^-3
    and then I make it 0 = 4x - 16^-3
    But there is no solution to that.
    So what is it classified as because my question is asking me to find maximum/minimum and any points of inflexion
    The 2nd derivative is f''(x) = 4 + 48^-4
    But I can't go further because there is no solution to x?
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  2. #2
    Senior Member
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    There are three roots to your derivative. 0=x(4-16x^2) now we know that 4-16x^2=(2-4x)(2+4x) so you have three solutions. these would be the turning points. I assume you can do the rest
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