List of top Mathematics Questions on Increasing and Decreasing Functions asked in MET

The values of \( a \), if \( f(x) = 2e^x - a e^{-x} + (2a+1)x - 3 \) increases for all \( x \), are in
If \( f(x) > 0 \; \forall x \in \mathbb{R} \), \( f'(3) = 0 \) and \( g(x) = f(\tan^2 x - 2\tan x + 4) \), \( 0 < x < \frac{\pi}{2} \), then \( g(x) \) is increasing in
The function $x^x$ is increasing, when
The length of the longest interval, in which $f(x)=3\sin x - 4\sin^3 x$ is increasing, is
The function \( y = -x^{2} + 6x - 3 \) is increasing when:

The function $y = -x^{2 + 6x - 3}$ is increasing when: