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Question Number 36927 by maxmathsup by imad last updated on 07/Jun/18

f i s a r e a l f u n c t i o n d e r i v a b l e o n [0, 1] / f (0) = 0 a n d f (1) = 1

p r o v e t h a t \forall n \in N \exists {(x_{i})}_{1 ⩽ i ⩽ n} s e q e n c e o f r e a l s w i t h x_{i} \neq x_{j} i f i \neq j

a n d \sum_{k = 1}^{n} f^{^{'}} (x_{k}) = n .