The maximum value of ( 1 x )^ 2 x² is

Step-by-step solution

Let f(x)= ( 1 x )^ 2 x² =x^ -2 x² array ll & f(x)=-2 x² x & 1 f(x) f^ (x)=-4 x x- 2 x² x & f^ (x)=x^ -2 x² [-4 x x-2 x] array For maximum, f^ (x)=0 x^ -2 x² [-4 x x-2 x]=0 -4 x x-2 x=0 x=- 1 2 x=e^ - 1 2 Again, f^ (x)=x^ -2 x² [-4 x x-2 x]²+x^ -2 x² [-4 x-4-2] f^ (e^ - 1 2 ) < 0 So, f(x) has maximum value at x=e^ - 1 2 f_ =f (e^ - 1 2 )= ( 1 1 e )^ 2 ( 1 e )² =( e )^ 2 ( 1 e ) =e^ 1 / e