Show that the function given by has maximum at x = e.

Question

Philoid · Accepted Answer

It is given that f(x) =

Then, f’(x) =

Now, f’(x) = 0

⇒ 1 - logx =0

⇒ log x =1

⇒ log x = log e

⇒ x = e

Now, f’’(x) =

Now, f’’(e)=

Therefore, by second derivative test, f is the maximum at x = e.