Math Problem Easy, PLLeeeaasse?

f(x) = x^4-2x^3

Find all relative extrema and points of inflection

1 Answer

  • Anonymous
    1 decade ago
    Favorite Answer

    The extrema will occur when the derivative is zero. So solve for x in

    4x^3-6x^2 = 0

    x^2*(4x-6) = 0 --> x = 0 or 3/2 could the x-coordinates of the extrema. BUT at x=0, it is not an extrema, it is only flat. So only at x=3/2 is it an extrema.

    Points of inflection can be the extrema of the derivative, or aka, where the double-derivative of the function is 0. So solve for x in:

    12x^2-12x = 0

    12x*(x-1) = x --> x = 0 or 1 are the x-coordinates of the points of inflection. Both these points are valid

    Source(s): math
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