$-{1/5}(x-4)^{5/3} - 2(x-4)^{2/3}$
I need to get this function into a simpler form so that I can analyze it's domain, limits, derivative and second derivative more easily. I am very bad with radicals and deriving in it's current state would be a nightmare. (Deriving is always a nightmare... but anyways).
Wolfram-Alfa has this as an alternate form: $y =-{1/5}(x-4)^{2/3}(x+6)$ but I have no idea how to obtain that from the original equation
Thanks for the help! :)
$$-\frac15(x-4)^{5/3} - 2(x-4)^{2/3}\underbrace{=}_{a^{5/3}=a^{1+2/3}=a\cdot a^{2/3}}-\frac15(x-4)(x-4)^{2/3} - 2(x-4)^{2/3}\\ \underbrace{=}_{\mathrm{common}\,\mathrm{factor}\, (x-4)^{2/3}}\left(-\frac15(x-4)-2\right)(x-4)^{2/3}=\left(-\frac x5+\frac 45-2\right)(x-4)^{2/3} \\=\left(-\frac x5-\frac 65\right)(x-4)^{2/3}=-\frac 15 (x+6)(x-4)^{2/3}.$$