1. Tardigrade
  2. Question
  3. Mathematics
  4. 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).

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Q. Let $f_N(x)$ be a polynomial function which satisfies $f^{\prime}{ }_N(x)=\prod\limits_{n=1}^N(x-n)^n$. If $n_1$ is sum of values of $x$ for which $f_{10}(x)$ attains maxima and $n_2$ denotes the sum of all values of $x$ for which $f _{10}( x )$ attains minima, then find the value of $\left( n _1+ n _2\right)$.

Application of Derivatives

Solution:

$f _{10}^{\prime}( x )=( x -1)( x -2)^2( x -3)^3 \ldots \ldots( x -10)^{10}$

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