Let fN(x) be a polynomial function which satisfies f prime N(x)= prod limitsn=1N(x-n)n. If n1 is sum of values of x for which f10(x) attains maxima and n2 denotes the sum of all values of x for which f 10( x ) attains minima, then find the value of ( n 1+ n 2).

Question

Let fN(x) be a polynomial function which satisfies f prime N(x)= prod limitsn=1N(x-n)n. If n1 is sum of values of x for which f10(x) attains maxima and n2 denotes the sum of all values of x for which f 10( x ) attains minima, then find the value of ( n 1+ n 2). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f 10 prime( x )=( x -1)( x -2)2( x -3)3 ldots ldots( x -10)10

Q. Let fN​(x) be a polynomial function which satisfies f′N​(x)=n=1∏N​(x−n)n. If n1​ is sum of values of x for which f10​(x) attains maxima and n2​ denotes the sum of all values of x for which f10​(x) attains minima, then find the value of (n1​+n2​).

f10′​(x)=(x−1)(x−2)2(x−3)3……(x−10)10

$f_{10}^{'} (x) = (x - 1) (x - 2)^{2} (x - 3)^{3} \dots\dots (x - 10)^{10}$