If f : R → R, f (x) is a differentiable bijective function, then which of the following is true?
Can’t be true as f (x) – x > 0 and f’(x) is decreasing. Then f (x) has to cut the line y = x.
Similarly, f (x) – x < 0 and f’(x) is increasing is not possible.
Also, f (x) – x ≠ 0 ⇒ f (x) = f -1(x) has no solution.
Find the interval of increase or decrease of the
The function f (x) = sin4 x + cos4 x increasing if:
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 (x) and g (x) are two positive and increasing function, then