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

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...
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 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 \( f(x) = \frac{k \sin x + 2 \cos x}{\sin x + \cos x} \) is strictly increasing for all real values of \( x \), then: 

\(\mathrm{f}(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0\) is strictly decreasing in

The function f defined by \(\mathrm{f}(x)=(x+2) \mathrm{e}^{-x}\) is

If \(2 \mathrm{f}(x)+3 \mathrm{f}\left(\frac{1}{x}\right)=x^2+1, x \neq 0\) and \(y=5 x^2 \mathrm{f}(x)\), then \(y\) is strictly 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 $f(x) = \frac{\lambda \sin x + 6 \cos x}{2 \sin x + 3 \cos x}$ is increasing, if
Function $f(x) = e^{-1/x}$ is strictly increasing for all $x$ where
$f(x) = \log|\sin x|$, where $x \in (0, \pi)$ is strictly increasing on
The function $f(x) = \cot^{-1} x + x$ is increasing in the interval.
The function \( f(x) = \log(1 + x) - \frac{2x}{2+x} \) is increasing on
If $f(x) = 2x^3 - 15x^2 - 144x - 7$, then $f(x)$ is strictly decreasing in
The function $f(x) = \cot^{-1} x + x$ is increasing in the interval.