Give the function: f(x)=(x−1)(x−2)^2 (x−3)^3 (x−4)^4 ...(x−2022)^(2022) Find extremes of f(x)¿


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Question Number 196710 by tri26112004 last updated on 30/Aug/23

$G i v e t h e f u n c t i o n :$ $f (x) = (x - 1) {(x - 2)}^{2} {(x - 3)}^{3} {(x - 4)}^{4} . . . {(x - 2022)}^{2022}$ $F i n d e x t r e m e s o f f (x) ¿$
Commented by mr W last updated on 30/Aug/23

$i {d o n}^{'} t t h i n k t h e y c a n b e e x a c t l y$ $d e t e r m i n e d, b e c a u s e w e {c a n}^{'} t e x a c t l y$ $s o l v e t h e e q u a t i o n f^{'} (x) = 0, i . e .$ $\ln ∣ x - 1 ∣ + 2 \ln ∣ x - 2 ∣ + 3 \ln ∣ x - 3 ∣ + . . . + 2022 \ln ∣ x - 2022 ∣= 0 .$
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