ClearAll;
f[x_]:= x^5 - x/2 + 1/2;
Plot[f[x],{x,0,1},PlotRange->{{0,1},{0,1}}]
findmin = FindMinimum[f[x],{x,0.5}]
globalminimizer = x/.Part[findmin,2]
globalmin = Part[findmin,1]