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Given y = x^4 − 4x^2 + 50. Find any extrema and any points of inflection

  • Math -

    f' = 4 x^3 -8 x = 4x (x^2-2)
    zero at x = 0 and x = sqrt 2 and x=-sqrt 2

    f" = 12 x^2 - 8

    at zero this is -8 so a maximum

    at +sqrt 2 this is +16
    same at -sqrt2 so those are minima

    Huge positive for x large positive and for x large negative

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