I'm trying to graph the equation $y=-2x^{2/3}(x-3)^{1/3}$.
I input the equation into WolframAlpha and it is asserting that the domain for the equation is $x \in R : x \geq 3$ and the range is $y \in R : y \leq 0$. It also says that there are two global maxima at $x=0$ and $x=3$. None of this information makes any sense to me. Graphing this equation in other programs gives me conflicting information. Is this a bug in WolframAlpha or is there something I'm missing?
Link to equation in WA: http://www.wolframalpha.com/input/?i=y%3D-2x%5E(2%2F3)(x-3)%5E(1%2F3)
It seems straight forward.
Wolfram alpha detected that when $x < 3$ you would be taking a root of a negative real number, and the first† such root is a complex number with a non-zero imaginary value and thus not an acceptable solution.
(† first as in: the root with the smallest non-negative angle from the real axis on the complex plane)
It's just not programmed to consider that the second of the three cube roots of a negative real is a negative real and thus an acceptable solution.
Programming bug. Ignore.
To resolve: y^2=-8*(x^3-3x^2)
Also plot y=2x^(2/3)(3-x)^(1/3)