Using ONLY calculus to prove that the minimum value of the function f(x)=|x-a1|+|x-a2|+|x-a3|+...+|x-a100| is f(a50) You are given a1<=a2<=a3<=.....<=a100.

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Using ONLY calculus to prove that the minimum value of the function f(x)=|x-a1|+|x-a2|+|x-a3|+...+|x-a100| is f(a50) You are given a1<=a2<=a3<=.....<=a100.

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yes..can u do it?
Nice problem! We will prove in general that the minimum value of \[f(x)=\sum_{k=1}^{2n}|x-a_k|\] where \(a_{k} n\). Hence \(f(x)\) attain its's minimum value at \(a_n\).
Hi, how about my answer above? :)

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very intuitive :) keep up. You are really good!

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