Question

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

Solution

Correct option is

 

Given,                  f (x) = sin x – x   

                           f’(x) = cos x – x                 

                    

    

∴ (x) is decreasing for   

Hence, maximum value of f (x) is at x = 0   

   

And minimum value of (x) is at    

SIMILAR QUESTIONS

Q1

 where 0 <x < π then the interval in which g(x) is decreasing is:   

Q2

Find the critical points for f (x) = (x – 2)2/3 (2x + 1).

Q3

 

Find all the values of a for which the function possess critical points.

 

Q4

 

Using calculus, find the order relation between x and tan-1x when x Ïµ [0, ∞). 

Q5

Using calculus, find the order relation between x and tan-1x when  

Q6

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:

Q7

 

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

Q8

The function  has a local maximum at x =

Q9

Find the set of critical points of the function  

              

Q10

  

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