Find All The Values Of A For Which The Function possess Critical Points.  

Where a is positive constant. Find the interval in which f’ (x) is increasing.

If a < 0, and f (x) = e^ax + e^–ax is monotonically decreasing. Find the interval to which x belongs.   

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).

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