For what values of $x$ is the function $f(x) = 2x^3 - 9x^2 + 12x + 29$ decreasing?

The function $f(x) = \tan^{-1}(\sin x + \cos x), x > 0$ is an increasing function in the interval.....

The function $f(x) = \frac{\ln(\pi+x)}{\ln(e+x)}$ is

The function $f(x) = \frac{\lambda \sin x + 3 \cos x}{2 \sin x + 6 \cos x}$ is monotonically increasing when:

Let $f(x) = \int_{x^2}^{x^2+1} e^{-t^2} dt$,for $x \in (-\infty, \infty)$. For which interval is $f(x)$ an increasing function?

Prove that the function $f$ given by $f(x) = \log |\cos x|$ is decreasing on $\left(0, \frac{\pi}{2}\right)$ and increasing on $\left(\frac{3\pi}{2}, 2\pi\right)$.