standard deviation~5 POINTS

C(x) = Total cost.
So Average cost, A = Total cost/no. of units produced = C(x)/x
= [16 sqrt x + x^2/343000]/x = 16/sqrt x + x/343000
dA/dx = - 8 x^(- 3/2) + 1/343000
Put dA/dx = 0, 8 x 343000 = x^(3/2) = 2744000
x = 19600.
d(dA/dx)/dx = 12 x ^(- 5/2) = 12/x^(5/2) = 12/(19600)^5/2 > 0, so it is a minimum.
So production level of x = 19600 will minimize the average cost.

2012-07-25 06:34:58 補充：
Curiosity : Why title of question is called 'standard deviation'? It has nothing to do with s.d.