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:
As, y = sin (f (x)) is monotonic for
∴ The maximum value of difference is π.
Then f decreases in the interval
Find the interval for which f (x) = x – sin x is increasing or decreasing.
Where a is positive constant. Find the interval in which f’ (x) is increasing.
If a < 0, and f (x) = eax + 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
where 0 <x < π then the interval in which g(x) is decreasing is: