Q. 24.7( 18 Votes )
Show that the function given by 
has maximum at x = e.
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.
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