Write the point where ( ) = e attains minimum value.

Question

Philoid · Accepted Answer

Let f (x)= x log_e x. Clearly f (x) is only defined for x >0.

For minimum value; f’(x)=0 and f’’(x)>0.

f’(x)= 1+lnx

⇒ x=1/e

f’’(x)= 1/x, Clearly f’’(x)>0 for all x. So only minima is defined.

So, minima of f (x) is at x = 1/e