Question 974804
{{{(d/dx)(x^2-x+1)^(1/3)}}}


{{{(1/3)(x^2-x+1)^(-2/3)(2x-1)}}}


{{{(2x-1)/(3(x^2-x+1)^(2/3))}}}


For any extremes value,
{{{(2x-1)/(3(x^2-x+1)^(2/3))=0}}}


The numerator now is what counts.
{{{2x-1=0}}}
{{{x=1/2}}}------------This is the best bet for y as a minimum value.  LOCAL minimum.