Problem 547 (difficulty: 4/10)

Prove that if \(\displaystyle f:[a,b]\to\R\) is continuous and \(\displaystyle x_1,x_2,\ldots,x_n\in[a,b]\), then there is a \(\displaystyle c\in[a,b]\), for which \(\displaystyle f(c)=\dfrac{f(x_1)+\dots+f(x_n)}{n}\).

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