For all real $x$,the minimum value of $\frac{1-x+x^2}{1+x+x^2}$ is

Let $f(x) = x^3 - 6x^2 + 12x - 3$. Then at $x = 2$,$f(x)$ has:

Maximum value of the function $f(x)=\frac{x}{8}+\frac{2}{x}$ on the interval $[1,6]$ is

Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by
$f_1(x) = \int_0^x \prod_{j=1}^{21}(t - j)^j dt, x > 0$
and
$f_2(x) = 2(x-1)^{50} - 25(x-1)^{48} + 2450, x > 0,$
where,for any positive integer $n$ and real numbers $a_1, a_2, \ldots, a_n$,$\prod_{i=1}^n a_i$ denotes the product of $a_1, a_2, \ldots, a_n$. Let $m_i$ and $n_i$,respectively,denote the number of points of local minima and the number of points of local maxima of function $f_i, i=1, 2$,in the interval $(0, \infty)$.
$(1)$ The value of $2m_1 + 3n_1 + m_1n_1$ is.
$(2)$ The value of $6m_2 + 4n_2 + 8m_2n_2$ is.
Find the values for $(1)$ and $(2)$.

What are the minimum and maximum values of the function $f(x) = x^5 - 5x^4 + 5x^3 - 10$?

The maximum value of $f(x) = \frac{\log x}{x}$ $(x > 0, x \neq 1)$ is