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

Statement $-1:$ The function $f(x) = x^2(e^x + e^{-x})$ is increasing for all $x > 0.$
Statement $-2:$ The functions $g(x) = x^2e^x$ and $h(x) = x^2e^{-x}$ are increasing for all $x > 0$ and the sum of two increasing functions in any interval $(a, b)$ is an increasing function in $(a, b).$

The function $f(x) = \frac{4x^3 - 3x^2}{6} - 2 \sin x + (2x - 1) \cos x$:

If $f(x) = \frac{1}{x + 1} - \log(1 + x)$,where $x > 0$,then what type of function is $f$?

For what value of $\lambda$ is the function $f(x) = \lambda x + \cos x$ strictly increasing?

If $f(x) = \log(1+x) - \frac{2x}{2+x}$,then $f(x)$ is increasing in