find the max. & min. value of f(x)=x ln²x

Hi Upendra,

f(x)=x ln²x ; x>0

f¹(x)=x 2 lnx (1/x) + ln²x

         = 2 ln x + ln²x = ln x (lnx+2)

for max or min f¹(x) = 0

     x=1 or e^-2

f¹¹(x) = 2/x + (2/x) ln x = (2/x)(lnx+1)

at x=1; f¹¹(x) = 2 >0

at x=e^-2 ; f¹¹(x) = -2 e²<0

therefore f(x) is max at x=e^-2

and minimum at x=1