f[s_] := s^2 and g[t_] := -(t - 1)^2 - 2 Using the equations from the theorem find the point (s0,t0) where the distance between the graphs is smallest. I want the point not the rules, that is use the {variables}/.Solve[{equations},{variables} syntax. You should get {{-(1/2^(2/3))+1/2^(1/3),1/2 (2+2^(1/3)-2^(2/3))},{-((1-I Sqrt[3])/(2 2^(1/3)))+(1+I Sqrt[3])/(2 2^(2/3)),-(1/4) I (4 I-I 2^(1/3)+I 2^(2/3)+2^(1/3) Sqrt[3]+2^(2/3) Sqrt[3])},{(1-I Sqrt[3])/(2 2^(2/3))-(1+I Sqrt[3])/(2 2^(1/3)),1/4 I (-4 I+I 2^(1/3)-I 2^(2/3)+2^(1/3) Sqrt[3]+2^(2/3) Sqrt[3])}}