Let $f_1:(0, \infty) \rightarrow R$ and $f_2:(0, \infty) \rightarrow R$ be defined by $f_1(x)=\int_0^x \prod_{j=1}^{21}(t-j)^j d t, x0$ and $f_2(x)=98(x-1)^{50}-600(x-1)^{49}+2450, x0$, where for any positive integer $n$ and real numbers $a_1, a_2, \ldots a_n, \Pi_{i=1}^n a_i$ 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 $(0, \infty)$ The value of $6 m_2+4 n_2+8 m_2 n_2$ is ________. [JEE Advanced 2021]

Question

Let $f_1:(0, \infty) \rightarrow R$ and $f_2:(0, \infty) \rightarrow R$ be defined by $f_1(x)=\int_0^x \prod_{j=1}^{21}(t-j)^j d t, x>0$ and $f_2(x)=98(x-1)^{50}-600(x-1)^{49}+2450, x>0$, where for any positive integer $n$ and real numbers $a_1, a_2, \ldots a_n, \Pi_{i=1}^n a_i$ 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 $(0, \infty)$ The value of $6 m_2+4 n_2+8 m_2 n_2$ is ________. [JEE Advanced 2021]

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Let \(f_1:(0, \infty) \rightarrow R\) and \(f_2:(0, \infty) \rightarrow R\) be defined by \(f_1(x)=\int_0^x \prod_{j=1}^…

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