Show that y = (a1 - x)^2 + (a2 - x)^2 +...+(an - x)^2 has an absolute minimum when x = (a1+a2+...=an)/n. I can usually do these but getting my head around the abstract problems can be a bit strenuous for me.
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The derivative with respect to x is 2(a1 - x) + 2(a2 - x) + ... + 2(an - x). Set that equal to 0 and solve for x. It will take about 2 lines.
x occurs n times, once in each of n expressions. So you have 2nx when you combine all those x terms.
x occurs n times, once in each of n expressions. So you have 2nx when you combine all those x terms.