Let 
and 
be defined by 
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 , …,a n , 
denotes the product of a 1 , a 2 , ....., a n . Let m 1 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, 
).
(i) The value of 6m 2 + 4n 2 + 8m 2 n 2 is_____
Text Solution
Verified by Experts6
(6)
f 2 '(x) = (98)(50)(x - 1) 49 - (600)(49)(x - 1) 48
= (49)(100)(x-1) 48 (x-1-6)
m 2 = 1,n 2 = 0
6m 2 + 4n 2 + 8m 2 n 2
6(1) + 4(0) + 8(0) = 6
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