How do you solve this? Please write clearly thank you! Let n > 1. Suppose that f has (n – 1)-th order continuous derivative and is n-times differentiable in R, and that f(x) = 0 has (n + 1) distinct...

How do you solve this? Please write clearly thank you!

Let n > 1. Suppose that f has (n – 1)-th order continuous derivative and is n-times differentiable in R, and that<br>f(x) = 0 has (n + 1) distinct roots x1 < x2 <……< xn+1· Show that there exists c E (a, b) such that<br>f(n) (c) = 0.<br>Hint: apply Rolle's Theorem for n times; or use induction on n to have a better proof structure.<br>

Extracted text: Let n > 1. Suppose that f has (n – 1)-th order continuous derivative and is n-times differentiable in R, and that f(x) = 0 has (n + 1) distinct roots x1 < x2=""><>< xn+1·="" show="" that="" there="" exists="" c="" e="" (a,="" b)="" such="" that="" f(n)="" (c)="0." hint:="" apply="" rolle's="" theorem="" for="" n="" times;="" or="" use="" induction="" on="" n="" to="" have="" a="" better="" proof="">

Jun 04, 2022

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How do you solve this? Please write clearly thank you! Let n > 1. Suppose that f has (n – 1)-th order continuous derivative and is n-times differentiable in R, and that f(x) = 0 has (n + 1) distinct...

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