List of top Mathematics Questions on Increasing and Decreasing Functions

Let \(f(x)=(a+2)x^{3}-3ax^{2}+9ax-5\). If \(f(x)\) is strictly decreasing for all \(x\in R\), then the interval in which \(a\) lies is
Let \(f(x)\) be the cubic polynomial having one of its roots as \(x=-1\). If \(f(0)=4,f'(0)=0,f^{''}(1)=0\), then...
The interval, in which the function \( f(x) = \frac{3}{x} + \frac{x}{3} \) is strictly decreasing, is :

Determine the interval(s) in which \(f(x)=5x^{3/2}-3x^{5/2}\), \(x>0\) is increasing.

Find the sub-interval of \((0, \infty)\) in which \(f(x) = x \log x\) is increasing.

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

The function \[ f(x)=2x+\cot^{-1}x+\log\!\left(\sqrt{1+x^2}-x\right) \] is
If $f(x) = \sqrt{3}\sin x - \cos x - 2ax + b$ decreases for all $x \in \mathbb{R}$, then:
If the real valued function \[ f(x)=\log(2x-3)-2x^2+6x-4 \] then the interval in which \(f(x)\) is increasing is
Let \(g(x) = f(x)+f(1-x)\) and \(f^{''}(x) < 0,0\leq x\leq 1\), then \(\ldots\)
If \(f(x) = log(1+x)-\frac{x}{1+x}\), then the values of \(x\) for which \(f(x)\) is monotonically increasing and monotonically decreasing are respectively.....
The function \(f(x) = tan^{-1}(sinx+cosx)\) is an increasing function in the interval.....
The value of \(k\) such that the function \(f(x) = sinx-cosx-kx+b\) is strictly decreasing for all real \(x\) 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 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 \(f(x)=x^3-3x^2+1\), 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 \( x \)