#f((3sqrt7)/7)=7((3sqrt7)/7)+9/((3sqrt7)/7)=6sqrt7#

#f(-(3sqrt7)/7)=-6sqrt7#

#rArr"stationary points at " ((3sqrt7)/7,6sqrt7)" and"#

#(-(3sqrt7)/7,-6sqrt7)#

#"to find the nature of the stationary points"#

#"use the "color(red)"second derivative test"#

#f'(x)=7-9x^-2#

#rArrf''(x)=18x^-3=18/x^3#

#f''((3sqrt7)/7)>0rArrcolor(red)" local minimum"#

#f''(-(3sqrt7)/7)<0rArrcolor(red)" local maximum"#

#rArr((3sqrt7)/7,6sqrt7)" is a local minimum"#

#"and " (-(3sqrt7)/7,-6sqrt7)" is a local maximum"# graph{7x+9x^-1 [-38.9, 38.88, -19.45, 19.45]}