c
\(U =\frac{- A }{ r ^{6}}+\frac{ B }{ r ^{12}}\)

\(F =-\frac{ dU }{ dr }=-\left( A \left(-6 r ^{-7}\right)\right)+ B \left(-12 r ^{-13}\right)\)

\(0=\frac{6 A }{ r ^{7}}-\frac{12 B }{ r ^{13}}\)

\(\frac{6 A }{12 B }=\frac{1}{ r ^{6}} \Rightarrow r =\left(\frac{2 B }{ A }\right)^{1 / 6}\)

\(U \left( r =\left(\frac{2 B }{ A }\right)^{1 / 6}\right)=-\frac{ A }{2 B / A }+\frac{ B }{4 B ^{2} / A ^{2}}\)

\(=\frac{- A ^{2}}{2 B }+\frac{ A ^{2}}{4 B }=\frac{- A ^{2}}{4 B }\)