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:

If f (x) = ax³ + bx² + cx + d where a, b, c, d are real numbers and 3b² < c², is an increasing cubic function and g(x) = af’ (x) + bf’’ (x) + c², then

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  

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