Find The Local Maximum And Local Minimum Of f (x) = x3 + 3x in [–2, 4].

If f : R → R, f (x) is a differentiable bijective function, then which of the following is true?

If f (x) and g (x) are two positive and increasing function, then

If the function y = sin (f (x)) is monotonic for all values of x (where f (x) is continuous), then the maximum value of the difference between the maximum and the minimum value of f (x), is: 

 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:

The function  has a local maximum at x =