Increasing and Decreasing Functions

The function $f\left(x\right)=x, x\in \mathrm{ℝ}$ has 

In which of the following intervals the function $f\left(x\right)=\sin x-\cos x$ is decreasing

The least value of $k$ for which the function $f\left(x\right)=x^2+kx+1$ is increasing on $[1,2]$ is

For all real values of $x$, the function $f\left(x\right)=\sin x-kx$ is decreasing when 

The function $f\left(x\right)=x^3-27x+8$ is increasing when

Find the intervals in which the function $f$ given by $f\left(x\right)=2x^2-3x$ is increasing.

Every invertible function is

Let $f\left(x\right)=x\tan x,$ where $0<x<\frac{\mathrm{\pi }}{2}$, then

The interval in which $f\left(x\right)=co{t}^{-1}x+x$ increases, is:

The roots of ${\left(x-41\right)}^{49}+{\left(x-49\right)}^{41}+{\left(x-2009\right)}^{2009}=0$ are:

If $f\left(x\right)$ is a differentiable real valued function satisfying $f^{\text{'}\text{'}}\left(x\right)-3f^{\text{'}}\left(x\right)>3, \forall x\ge 0$ and $f^{\text{'}}\left(0\right)=-1$, then $f\left(x\right)+x, \forall x>0$ is

If $x_1, x_2\in \left(0, \frac{\pi }{2}\right)$, then $\frac{\tan x_2}{\tan x_1}$ is (where $x_1<x_2$)

If $x\in (0,\frac{\pi }{2})$, then the function $f\left(x\right)=x\sin x+\cos x+{\cos }^{2}x$ is:

The function $f\left(x\right)=x^2-2ax+6$ is strictly increasing for $x>0$, when

The interval on which the function $f\left(x\right)=2x^3+9x^2+12x-1$ is decreasing is

Which of the following functions is decreasing on $\left(0, \frac{\mathrm{\pi }}{2}\right)$?

 The function $\mathrm{f}\left(\mathrm{x}\right)=4{\sin }^3\mathrm{x}-6{\sin }^2\mathrm{x}+12\mathrm{sinx}+100$ is strictly

$\mathrm{y}=\mathrm{x}(\mathrm{x}-3{)}^2$ decreases for the values of $\mathrm{x}$ given by:

The interval in which $y=x^2{e}^{-x}$ is strictly increasing is

On which of the following intervals is the function $f$ given by $f\left(x\right)=x^{100}+\sin x-1$ is strictly decreasing?