Mathematics - Application of Derivative Question with Solution | TestHub

Let $f_1:(0,\infty )\to \mathbb{R}$ and $f_2:(0,\infty )\to \mathbb{R}$ be defined by $$f_1(x)={\int }_0^x\prod _{j=1}^{21}(t-j{)}^{j}dt,x>0$$ and $f_2(x)=98(x-1{)}^{50}-600(x-1{)}^{49}+2450,x>0$ where, for any positive integer $n$ and real numbers $a_1,a_2,\dots ,a_n,{\prod }_{i=1}^n{a}_i$ denotes the product of $a_1,a_2,\dots ,a_n.$ 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 $(0,\infty )$. The value of$2m_1+3n_1+m_1{n}_1$is _____.