# Thread: property of cost function

1. ## property of cost function

I consider a real valued fanction C(q) such that

C(q) is continious, increasing, concave on the closed interval [0,Q] in R1, C(0)=0, C'(0)=0.

Does it imply that
C'(q)/C''(q)->0 when q->0 ?

2. Yes. The condition that the curve is concave over the entire interval means c''(0) is finite. Thus c'(0)/c''(0) = 0.