$\therefore $ New component are $(3,-2,7).$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f_1(x)=\int_0^x \prod_{j=1}^{21}( t - j )^{ j } dt , x >0$
and
$f_2(x)=98(x-1)^{50}-600(x-1)^{39}+2450, x>0,$
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 $(0, \infty)$
($2$) The value of $2 m_1+3 n_1+m_1 n_1$ is. . . . . .
($2$) The value of $6 m _2+4 n _2+8 m _2 n _2$ is. . . . . .
Give the answer or quetion ($1$) and ($2$)