Let \( f_{1}:(0, \infty) \rightarrow R \) and \( f_{2}:(0, \infty) \rightarrow R \) be defined b... VIDEO
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 \( a_{1}, a_{2}, \ldots a_{n}, \prod_{i=1}^{n} a_{i} \) 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 \( (0, \infty) \)
The value of \( 2 m_{1}+3 n_{1}+m_{1} n_{1} \) is
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