y= x^(1/x)lny = (1/x)lnx(1/y) dy/dx = ( 1/x^2)(1 - lnx)dy/dx =(1-lnx). x^(1/x -2 )y'=01-lnx =0x=edy/dx | x=e+ <0dy/dx | x=e- >0x=e (max)max y = y(e)= e^(1/e)
