#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]}