Question 436809
{{{dC/dx = x - 0.9}}}  Set to zero: x - 0.9 = 0 ==> x = 0.9. ==> An extremum exists at x = 0.9.
{{{d^2C/dx^2 = 1 > 0}}} ==> the extremum at  x = 0.9 is a(n) (absolute) minimum, by the 2nd derivative test. 
Hence to minimize average cost, build 0.9*100 = 90 bicycles.