Calculous

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let f be the function defined by f(x)=12x^2/3 -4X
a)find the intervals on which f is increasing
I got the rest of the question but I'm still not getting the increasing/decreasing thing

  • Calculous -

    As we saw in a previous posting, f(x) is increasing where f'(x) is positive.

    A positive slope means that when x increases, f(x) increases. A negative slope means that as x increases, f(x) decreases.

    f'(x) = 8x^(-1/3) - 4

    So, we want 8/x^1/3 - 4 > 0
    8/x^1/3 > 4
    1/x^1/3 > 1/2
    x^1/3 > 2
    x > 8

  • Calculus - Correction -

    Oops. Taking reciprocals reverses the direction of the inequality:

    8/x^1/3 - 4 > 0
    8/x^1/3 > 4
    1/x^1/3 > 1/2
    x^1/3 < 2
    x < 8

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