Let f (x) = Sin x – x on [0, π/2], Find Local Maximum And Local Minimum.

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

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

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

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

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

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

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

The function  has a local maximum at x =

Find the set of critical points of the function  

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