math

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f(x)=x^4-4x^3+10

Where are the relative extrema, if they exist?

  • math -

    from your previous post

    x = 0 or x = 3

    so
    f(0) = 10
    f(3) = 81 - 108 + 10 = -17

    f '' (x) = 12x^2 - 24x

    f '(0) = f ''(0) = 0
    so (0,10) is a point of inflection

    f ''(3) = 108 - 72 > 0
    so at (3,-17) the curve is concave upwards, so
    (3,-17) is a minimum point

    look at the sketch

    http://www.wolframalpha.com/input/?i=plot+x%5E4-4x%5E3%2B10

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