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} d t, \quad x > 0 $ and f_{2}(x)=98(x-1)^{50}-600(x-1)^{49}+2450, \quad x > 0 $where,foranypositiveinteger$n$andrealnumbers$a_{1}, a_{2}, \ldots, a_{n}, \prod_{i=1}^{n} a_{i}$denotestheproductof$a_{1}, a_{2}, \ldots, a_{n} .$Let$m_{i}$and$n_{i}$,respectively,denotethenumberofpointsoflocalminimaandthenumberofpointsoflocalmaximaoffunction$f_{i}, i=1,2$,intheinterval$(0, \infty)$. The value of$6m_2+4n_2+8m_2{n}_2$is ____.