The function $f(x) = ax + b$ is strictly increasing for all real $x$ if

Let $f(x) = \int {e^x}(x - 1)(x - 2)dx$. Then $f$ decreases in the interval

If $x > 0$,then $\frac{x}{1+x} - \log(1+x)$

The function $f(x) = (x(x - 2))^2$ is an increasing function on the set.....

Define $f(x) = \frac{1}{2}[|\sin x| + \sin x]$, $0 < x \leq 2\pi$. Then, $f$ is

Let $\lambda^{*}$ be the largest value of $\lambda$ for which the function $f_{\lambda}(x) = 4\lambda x^{3} - 36\lambda x^{2} + 36x + 48$ is increasing for all $x \in \mathbb{R}$. Then $f_{\lambda^{*}}(1) + f_{\lambda^{*}}(-1)$ is equal to: