Question

Use the function (x) = x1/xx > 0 to determine the bigger of the two numbers.

Solution

Correct option is

  

Taking log on both sides we have

                       

Differentiating both sides we have

                       

  

   

or                       x = e   

  

   

'f ' has a maximum at x = e.   

But x = e is the only extreme value.   

∴ f has the greatest value at x = e  

   

SIMILAR QUESTIONS

Q1

The set of all values of ‘b’ for which the function (x) = (b2 – 3b + 2) (cos2x – sin2x) + (b – 1) x + sin 2 does not possesses stationary points is:

Q2

 

Find the local maximum and local minimum of (x) = x3 + 3x in [–2, 4].

Q3

The function  has a local maximum at x =

Q4

Find the set of critical points of the function  

              

Q5

Let (x) = sin x – x on [0, π/2], find local maximum and local minimum.

Q6

  

Then find the value of ‘a’ for which (x) has local minimum at x = 2.

Q7

  

Discuss maxima and minima.

 

Q8

A cubic (x) vanishes at x = –2 and has relative maximum/minimum x = –1 and   Find the cubic (x). 

Q9

 

Find the maximum and minimum value of  

                      

Q10

 

The maximum value of