$f(x)=x^6(x-7)^3$ over the range $[-14, 10]$ Where does the function achieve its global minimum?
I've identified the global min as $14/3$ and was told this was incorrect. I tried its corresponding y value as well and received the same answer. Other critical points are $7$ and $0$ and they are also incorrect. 

In $x=\frac{14}{3}$, $f$ achieve local minimun, note that
$f(-4)=(-4)^{6}(-4-7)^{3}= -5. 451\,8\times 10^{6}$
$f(14/3)=(14/3)^{6}(14/3-7)^{3}=-\frac{2582\,630\,848}{19\,683}=-1.312\,1\times 10^{5}$
