The function $f(x) = 2x^3 - 9x^2 + 12x + 29$ is monotonically decreasing when:

If $f(x) = \sin x - \cos x - ax + b$ is a decreasing function for all $x \in R$,then:

Let $f(x) = \frac{x}{\sqrt{a^2 + x^2}} - \frac{d - x}{\sqrt{b^2 + (d - x)^2}}$,$x \in R$,where $a, b$ and $d$ are non-zero real constants. Then:

If $f''(x)$ is a positive function for all $x \in R$,$f'(3) = 0$ and $g(x) = f(\tan^2 x - 2 \tan x + 4)$ for $0 < x < \frac{\pi}{2}$,then the interval in which $g(x)$ is increasing is

If $f(x) = x^2 + kx + 1$ is a strictly increasing function on the interval $[1, 2]$,then what is the minimum value of $k$?

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