Question
Given the constants $a_1, a_2, \ldots, a_n$, find the value of $x$ that guarantees that the sum$$S(x)=\left(a_1-x\right)^2+\left(a_2-x\right)^2+\cdots+\left(a_n-x\right)^2$$will be as small as possible.
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.. + (aₙ-x)². Show more…
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Given $n$ numbers $x_{1}, \ldots, x_{n},$ find the value of $x$ minimizing the sum of the squares:$$\left(x-x_{1}\right)^{2}+\left(x-x_{2}\right)^{2}+\cdots+\left(x-x_{n}\right)^{2}$$ First solve for $n=2,3$ and then try it for arbitrary $n$
APPLICATIONS OF THE DERIVATIVE
Applied Optimization
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