a. For what value of c is the quantity ?(xi – c)2minimized? [Hint: Take the derivative with respect to c, set equal to 0, and solve.] b. Using the result of part (a), which of the two quantities )?

Answer: Step1: 2 a). Given that, for what value of c is the quantity (x c) miiimized. 2 Let S = (x c)i Differentiate with respect to ‘c’. That is, ds d 2 dc = dc((x ic) ) ds d 2 dc = dc (x i c) ) ( therefore, the formula for d x = nx n1 ) dx So that, ds 21 d dc = 2 (x i) dc (- c) = 0 = 2 (x i) ( 1)= 0 = 2 (x ci = 0 = (x ic)= 0 = x c= 0 i = x inc = 0 nc = x i xi c = n c = x Therefore, c = x. Step2: b). In result (a), we solved that c = x. 2 c = x minimizes (x c) .i 2 2 Then, (x xi < (x ) i