Let f1:(0,∞)→R and f2:(0,∞)→R be defined by f1(x)=∫x021∏j=1(t−j)jdt, x>0 and f2(x)=98(x−1)50−600(x−1)49+2450, x>0, where, for any positive integer n and real number a1,a2…an, n∏i=1ai denotes the product of a1,a2,...an. Let mi and ni respectively denote the number of points of local minima and the number of points of local maxima of function fi, i=1,2 in the interval (0,∞).The value of 2m1+3n1+m1n1 is

Let f1:(0,∞)→R and f2:(0,∞)→R be defined by f1(x)=∫x021∏j=

1.	Let f1:(0,∞)→R and f2:(0,∞)→R be defined by f1(x)=∫x021∏j=1(t−j)jdt, x>0 and f2(x)=98(x−1)50−600(x−1)49+2450, x>0, where, for any positive integer n and real number a1,a2…an, n∏i=1ai denotes the product of a1,a2,...an. Let mi and ni respectively denote the number of points of local minima and the number of points of local maxima of function fi, i=1,2 in the interval (0,∞).The value of 2m1+3n1+m1n1 is
Answer» Let $f_{1} : (0, \infty) \to R$ and $f_{2} : (0, \infty) \to R$ be defined by $f_{1} (x) = \int_{0}^{x} 21 \prod j = 1 (t - j)^{j} d t,$ $x > 0$ and $f_{2} (x) = 98 (x - 1)^{50} - 600 (x - 1)^{49} + 2450,$ $x > 0,$ where, for any positive integer $n$ and real number $a_{1}, a_{2} \dots a_{n},$ $n \prod i = 1 a_{i}$ denotes the product of $a_{1}, a_{2}, . . . a_{n} .$ 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