$f(x) = x^2 - 6x + 10$ is an increasing function in the . . . . . . interval.

The function $f(x) = 2{x^3} + 18{x^2} - 96x + 45$ is an increasing function when:

The real valued function $f(x) = \frac{x^2}{2} - \log(x^2 + x + 1)$ is

Let $g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)$ and $f^{\prime \prime}(x)>0$ for all $x \in(0,3)$. If $g$ is decreasing in $(0, \alpha)$ and increasing in $(\alpha, 3)$,then $8 \alpha$ is

For every value of $x$,the function $f(x) = e^x$ is:

The function $f(x) = x e^{x(1-x)}, x \in R$,is