List of top Mathematics Questions on Increasing and Decreasing Functions

The function \[ f(x)=2x+\cot^{-1}x+\log\!\left(\sqrt{1+x^2}-x\right) \] is

Find the interval(s) in which the function $f(x) = \frac{x}{\log x}$, where $x \in (0, 1) \cup (1, \infty)$, is increasing.

Find the sub-intervals of \[ (0,\pi) \] in which \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

Find the sub-interval of \[ (0,\infty) \] in which \[ f(x)=x^2e^{-x} \] is increasing.

Let $f(x) = \frac{1}{3\sqrt{x}}(\frac{2}{x} - 3), x > 0$. Then $f(x)$ is decreasing in}

Let \(f(x) = -x^3 + 9x^2 - \alpha x - 13\), where \(x \in \mathbb{R}\) and \(\alpha\) is a constant. If the function \(f\) is increasing only in the interval (1,5), then the value of \(\alpha\) is equal to

Let \(f : [-\frac{\pi}{2}, \frac{\pi}{2}] \rightarrow (-\infty, \infty)\) be given by \(f(x) = \tan(x)\sin(x)\). Then \(f(x)\) is

The function \[ y=\frac{\sin x+2\cos x}{3\sin x+4\cos x} \] is

If the real valued function \[ f(x)=\log(2x-3)-2x^2+6x-4 \] then the interval in which \(f(x)\) is increasing is

If displacement of particle moving in straight line is \[ S=t^3-3t^2+3t-4 \] then time interval in which \(S\) is increasing is

If $f(x) = \sqrt{3}\sin x - \cos x - 2ax + b$ decreases for all $x \in \mathbb{R}$, then:

The interval, in which the function \( f(x) = \frac{3}{x} + \frac{x}{3} \) is strictly decreasing, is :

If \(f(x)=x^3-3x^2+1\), then the interval in which the function is decreasing is:

The function \[ f(x)=e^{ax}+e^{-ax}, \quad x\in R \] and \(a<0\), is strictly decreasing for all values of \(x\), where:

Let $f$ and $g$ be differentiable real valued functions on $[0,\infty)$. If $f$ is increasing, $g$ is decreasing and $h(x)=f(g(x))$, then $h(2026)-h(2025)$ is

Find the value of \( k \) if the function \( f(x) = k\sin x + 2\cos x \) is increasing for all \( x \)

Find the value of \( k \) if the function \( f(x) = \dfrac{k\sin x + 2\cos x}{\sin x + \cos x} \) is increasing for all \( x \).

If $g(x)=x^{2}-x, x\in\mathbb{R},$ then $g(x)$ is increasing in ________.

If $f(x) = \log(1 + x) - \frac{2x}{2 + x}$, then $f(x)$ is increasing in ______.

The function $f(x)=[x(x-2)]^{2}$ is increasing in the set}

In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is

The function $f(\theta)=\sin \theta+\cos \theta,\ 0\leq \theta \leq 2\pi$ is decreasing in the interval:

The function $f(x)=e^x-x$ is increasing in the interval:

The function \( f(x) = 2x^3 - 3x^2 - 36x + 28 \) is increasing in